Answer:
The given matrix equation can be written as:
[2 3; 1 2] * [x; y] = [5; 4]
Multiplying the matrices on the left side of the equation gives us the system of equations:
2x + 3y = 5 x + 2y = 4
To solve for x and y using matrices, we can use the inverse matrix method. First, we need to find the inverse of the coefficient matrix [2 3; 1 2]. The inverse of a 2x2 matrix [a b; c d] can be calculated using the formula: (1/(ad-bc)) * [d -b; -c a].
Let’s apply this formula to our coefficient matrix:
The determinant of [2 3; 1 2] is (22) - (31) = 1. Since the determinant is not equal to zero, the inverse of the matrix exists and can be calculated as:
(1/1) * [2 -3; -1 2] = [2 -3; -1 2]
Now we can use this inverse matrix to solve for x and y. Multiplying both sides of our matrix equation by the inverse matrix gives us:
[2 -3; -1 2] * [2x + 3y; x + 2y] = [2 -3; -1 2] * [5; 4]
Solving this equation gives us:
[x; y] = [-7; 6]
So, the solution to the system of equations is x = -7 and y = 6.
4. What is/are the basis (bases) for directional hearing? a. Differences in the intensity of sound at the two ears b. Differences in the arrival time of sound at the two ears c. Differences in the timbre of the sound at the two ears d. Differences in the arrival time and the intensity of the sound at the two ears Sensory organs 5. What are the primary function(s) of the outer hair cells? a. Send information about sound to the brain b. Outer hair cells act as motors that increase the sensitivity of the ear c. Outer hair cells are sensitive to head movements d. The way the outer hair cells are innervated determine their function
4. The basis for directional hearing involves differences in the arrival time and the intensity of the sound at the two ears.
5. The primary function of the outer hair cells is to act as motors that increase the sensitivity of the ear.
4. The basis for directional hearing involves differences in the arrival time and the intensity of the sound at the two ears.
This means that the brain processes the information from both ears and determines the location of the sound based on these differences.
When sound reaches one ear before the other, it provides the brain with a cue for determining the direction of the sound.
Additionally, the brain can determine the direction of sound by comparing the intensity of sound at both ears.
5. The primary function of the outer hair cells is to act as motors that increase the sensitivity of the ear.
The primary function of the outer hair cells is to act as motors that increase the sensitivity of the ear. These cells can amplify the sound that enters the ear by changing their shape in response to sound waves.
This amplification helps to improve the overall sensitivity of the ear and allows for better detection of soft sounds.
Additionally, the outer hair cells are sensitive to head movements and can help to adjust the way that sound is processed in the ear.
The way that the outer hair cells are innervated can also determine their function and how they contribute to the overall function of the ear.
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Translate this phrase into an algebraic expression.
67 decreased by twice Jenny's savings
Use the variable j to represent Jenny's savings.
Answer:
67-2j
Step-by-step explanation:
thats all i got for you my friend
Find x from this equation 7x-5=10-3x
Answer:
x=1.5
Step-by-step explanation:
7x-5=10-3x <=>7x+3x=10+5 <=> 10x=15 <=> x= 3/2 = 1.5
ok done. Thank to me :>
ABCD is a rhombus. If the area of the rhombus is 16 cm2, and = 8 cm, what is ?
1 cm
4 cm
2 cm
8 cm
Need some help!! Just a brief complete sentence will be great!
Given function is,
\(y=\sqrt[]{x+2}-3\)To find the Horizontal and vertical shift.
Horizontal shift is defined as any changes which is made by adding or substracting to the variable x in the function.
Vertical shift is defined as any changes which is made by adding or substracting to the variable y in the function.
So in the given function the value inside the root is ( x+2 ). so the horizontal shift is two unit left side.
So in the given function the value out side the root is -3, which directly add it to the variable y.
So the vertical shift is three unit down ( Downwards since negative side ).
So the required answer is 2 units left side and 3 units downwards.
Factories (x+2y)^3+(x-2y)^3
With full explanation
Answer:
\(\boxed{=2x(x^2+6y^2)}\)
Step-by-step explanation:
Remember:
\((a+b)(a-b)=a^2-b^2\\\\a^3+b^3=(a+b)(a^2-ab+b^2)\\\\\\(x+2y)^3+(x-2y)^3\\\\=(x+2y+x-2y)((x+2y)^2-(x+2y)(x-2y)+(x-2y)^2)\\\\=2x(x^2+4xy+4y^2-(x^2-4y^2)+x^2-4xy+4y^2)\\\\=2x(x^2+6y^2)\\\)
the circle passes through the point (-4,-1)(−4,−1)left parenthesis, minus, 4, comma, minus, 1, right parenthesis. what is its radius? choose 1 answer: choose 1 answer: (choice a) a 2.52.52, point, 5 (choice b) b \sqrt{2} 2 square root of, 2, end square root (choice c) c 1.51.51, point, 5 (choice d) d \sqrt{3} 3
To find the radius of a circle that passes through a given point, we can use the distance formula.
The distance between the center of the circle and the given point will be equal to the radius. Let's assume the center of the circle is (h, k), and the given point is (-4, -1). The distance between these two points can be calculated using the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Substituting the values, we get:
d = sqrt((-4 - h)^2 + (-1 - k)^2)
Since the circle passes through the point (-4, -1), this means that the distance between the center and the point should be equal to the radius. So, we can set up the equation:
sqrt((-4 - h)^2 + (-1 - k)^2) = r
where r is the radius.
We can simplify this equation by squaring both sides:
(-4 - h)^2 + (-1 - k)^2 = r^2
Now, we need more information or equations to solve for the radius. Without additional equations or the values of h and k, we cannot determine the exact value of the radius.
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In this case, the circle is degenerate, meaning it is just a single point and does not have a meaningful radius. So, none of the given choices (a), (b), (c), or (d) are correct.
The radius of a circle can be determined by finding the distance between the center of the circle and any point on its circumference. In this case, we are given the point (-4,-1) that lies on the circle's circumference. To find the radius, we need to determine the distance between this point and the center of the circle.
The center of the circle is not given explicitly, so we need to use the information provided to determine it. Since the circle passes through the point (-4,-1), we can conclude that the center of the circle is equidistant from this point and any other point on the circumference.
To find the center, we can select another point on the circumference and calculate its distance from (-4,-1). Let's say we choose a point on the circle with coordinates (x,y). The distance between (-4,-1) and (x,y) is given by the distance formula:
\(d = /sqrt((x - (-4))^{2} + (y - (-1))^{2})\)
Since the center is equidistant from any point on the circumference, we can write the equation:
\(/sqrt((x - (-4))^{2} + (y - (-1))^{2}) = r\)
where r is the radius.
Now we substitute the given point (-4,-1) into the equation:
\(/sqrt((-4 - (-4))^{2} + (-1 - (-1))^{2}) = r\)
Simplifying the equation, we get:
\(/sqrt(0^{2} + 0^{2}) = r\)
Therefore, the radius of the circle is 0.
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select all that apply stem-and-leaf diagrams can be used to multiple select question. determine how dispersed the data are. observe individual data points. analyze the shape of the data. analyze qualitative data.
Stem and leaf diagrams can be used to analyze the shape of the data, determine how dispersed the data are, and observe individual data points.
The options given to us are:
1. Determine how dispresed the data are
2. Observe individual data points
3. Analyze the shape of the data
4. Analyze quantitative data
A stem and leaf plot, also known as a stem and leaf diagram, is a way to arrange data so that it is simple to see how frequently various sorts of values occur. It is a graph that displays ordered numerical data. A stem and a leaf are divided into each piece of data.
A stem and leaf plot is shown as a customised table with the first or final digit of each data value divided into a stem and the remaining digit in a leaf. The stem and leaf plot key is the symbol " | " that is used to display the stem and leaf values.
This, here, the right options are:
Option #1: Determine how dispresed the data are
Option #2: Observe individual data points
Option #3: Analyze the shape of the data
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Stem and leaf diagrams can be used to analyze the shape of the data, determine how dispersed the data are and observe individual data points.
The options given to us are:
1. Determine how dispersed the data are
2. Observe individual data points
3. Analyze the shape of the data
4. Analyze quantitative data
A stem and leaf plot, also known as a stem and leaf diagram, is a way to arrange data so that it is simple to see how frequently various sorts of values occur. It is a graph that displays ordered numerical data. A stem and a leaf are divided into each piece of data.
A stem and leaf plot is shown as a customised table with the first or final digit of each data value divided into a stem and the remaining digit in a leaf. The stem and leaf plot key is the symbol " | " that is used to display the stem and leaf values.
This, here, the right options are:
Option #1: Determine how dispresed the data are
Option #2: Observe individual data points
Option #3: Analyze the shape of the data
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Name all the different types of factoring. Explain, in words, how to do each one.
And then give an example for each. (You do not have to solve your example).
At the beginning of spring, Sophia planted a small sunflower in her backyard. When it was first planted, the sunflower was 25 inches tall. The sunflower then began to grow at a rate of 3 inches per week. How tall would the sunflower be after 9 weeks? How tall would the sunflower be after ww weeks?
Height after 9 weeks:
Height after ww weeks:
The height of the sun flower after w weeks is 25 + 3w inches and the height of flower after 9 weeks is 52 inches.
How to find the height of flowers?At the beginning of spring, Sophia planted a small sunflower in her backyard. When it was first planted, the sunflower was 25 inches tall.
The sunflower then began to grow at a rate of 3 inches per week.
The height of the flowers after w weeks can be calculated using the equation below:
height of flower after w weeks = 25 + 3w
The height of the flower after 9 weeks can be calculated as follows:
height of flower after 9 weeks = 25 + 3(9)
height of flower after 9 weeks = 25 + 27
height of flower after 9 weeks = 52 inches
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11) Ryan and three friends went to Fridays the bill was $123,42 If they gave an 18 percent tip, how much did they have to pay if they divided the total bill equally?
the chi-square distribution provides a good approximation to the sampling distribution of the chi-square statistic if the expected frequency in each cell is
The chi-square distribution provides a good approximation to the sampling distribution of the chi-square statistic if the expected frequency in each cell is at least 5.
The chi-square statistic is a measure of how different an observed frequency is from the expected frequency. It is calculated by taking the difference between the observed and expected frequency in each cell, squaring it, and then summing the results. This measure can then be compared to a chi-square distribution with degrees of freedom equal to the number of cells minus one. If the calculated statistic is larger than the expected value from the chi-square distribution, then it can be concluded that the observed frequency differs significantly from the expected frequency.
In order to use the chi-square approximation, it is important that the expected frequency in each cell is at least 5. This is because the chi-square approximation only works well when there are large expected frequencies. When expected frequencies are smaller than 5, the chi-square statistic is not an accurate measure of the difference between the observed and expected frequencies.
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x -3y =12 in slope-intercept form
Answer:
y = (1/3)x - 4
Step-by-step explanation:
put y on one side
x -3y =12
y =12-x/-3
y=12/-3 -x/-3
y=-4 + 1/3x
chatgpt
HELP PLEASE I DONT KNOW THIS.
The two adjacent angle according to the given question are angle 1 (60 degree) and angle 5 ( 30 degree)
what is adjacent angle?
In geometry, an adjacent angle refers to an angle that shares a common vertex and a common side with another angle. The word "adjacent" means "next to" or "near to." Therefore, two angles are adjacent if they are next to each other and share a side. When two adjacent angles are added together, they form a larger angle known as a linear pair. Adjacent angles are important in many areas of geometry, including trigonometry, where they are used to calculate the values of trigonometric functions such as sine, cosine, and tangent. In real-life applications, adjacent angles can be found in various geometric shapes, such as triangles, rectangles, and polygons, and are used to determine the measurements and properties of these shapes.
Adjacent angles are important in geometry and are used to calculate the values of trigonometric functions such as sine, cosine, and tangent.
Therefore, The two adjacent angle according to the given question are angle 1 (60 degree) and angle 5 ( 30 degree)
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Write the equation of the graph shown below in factored form. a graph that starts at the top left and continues down through the x axis at negative four to a minimum around y equals negative two point eight and goes up to touch the x axis at negative two and then goes back down to a minimum around y equals negative zero point four and then goes back up to cross the x axis at negative one.
The equation of the graph shown can be written in factored form as follows:
y = a(x - h)(x - k)(x - m)
To find the equation, we need to identify the x-intercepts and the minimum point of the graph.
From the description, we know that the graph starts at the top left and continues down through the x-axis at x = -4. This means that one of the factors is (x + 4).
Next, the graph reaches a minimum around y = -2.8. This indicates that the graph touches the x-axis at this point, so another factor is (x + 2).
Moving forward, the graph goes back down to another minimum around y = -0.4. Again, this means the graph touches the x-axis at this point. So we have another factor, (x + 1).
Now we have all the necessary factors: (x + 4), (x + 2), and (x + 1). To determine the coefficient "a," we can use the fact that the graph goes up after crossing the x-axis at x = -2. This suggests that "a" must be positive.
Therefore, the equation of the graph in factored form is:
y = a(x + 4)(x + 2)(x + 1)
Please note that without specific points, it is not possible to determine the exact value of "a" or the precise shape of the graph. The equation provided represents a general equation that satisfies the given conditions.
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Lindsey is working really hard to improve her grade. on her first quiz she scored 67 point, on her second she scored 71, and on her third she scored 75. her scores continue to increase at the same rate. write a recursive and explicit formula for this geometric sequence.
The recursive formula for Lindsey's scores is aₙ = aₙ₋₁ \(\times\) r, and the explicit formula is aₙ \(= 67 \times r^{(n-1).\)
To find the recursive and explicit formulas for the given geometric sequence, let's analyze the pattern of Lindsey's scores.
From the given information, we can observe that Lindsey's scores are increasing at the same rate.
This suggests that the scores form a geometric sequence, where each term is obtained by multiplying the previous term by a common ratio.
Let's denote the first term as a₁ = 67 and the common ratio as r.
Recursive Formula:
In a geometric sequence, the recursive formula is used to find each term based on the previous term. In this case, we can write the recursive formula as:
aₙ = aₙ₋₁ \(\times\) r
For Lindsey's scores, the recursive formula would be:
aₙ = aₙ₋₁ \(\times\) r
Explicit Formula:
The explicit formula is used to directly calculate any term of a geometric sequence without the need to calculate the previous terms.
The explicit formula for a geometric sequence is:
aₙ = a₁ \(\times r^{(n-1)\)
For Lindsey's scores, the explicit formula would be:
aₙ \(= 67 \times r^{(n-1)\)
In both formulas, 'aₙ' represents the nth term of the sequence, 'aₙ₋₁' represents the previous term, 'a₁' represents the first term, 'r' represents the common ratio, and 'n' represents the term number.
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How do you determine if a table represents a linear function?
To check the if a table represents a linear function we have to find the rate of change between the first two ordered pairs can be compared to the rate of change between the first and last ordered pairs to see if they are the same.
Well, a straight line is proportional to a linear function (on a graph). And the answers to the numbers can't be the same. If the X input is 5, for instance, and the Y output is 7, then Another non-linear X input of 5 and Y output of 8 follows.
What is linear function?The terms "linear function" in mathematics apply to two different but related ideas: A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.
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suppose a hypothesis test, using α = 0.05, is being conducted with the following null hypothesis: h0: μ = 2. which one of the following confidence intervals would lead to rejecting the null hypothesis
A confidence interval cannot instantly lead to rejecting the null hypothesis in a hypothesis test. In the given case the null hypothesis is either rejected or rejected based on test statistics.
α = 0.05
μ = 2
If the confidence interval is 1.0 or 2.0, then the null hypothesis value of 2 drops exceeds the interval, this makes the data contradict the null hypothesis and may reject the null hypothesis.
This alone would not be good to decline the null theory - the conclusion to reject or not reject the null hypothesis is determined by the test statistic and the alternate p-value.
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Solve for x: -4x - 4 = -4(x + 2)
Oo
O-4
O All real numbers
O No solution
the ratio of width to the length is 2 : 7 if the width of the the window is 3 feet then what is the length
Answer:
I think it's 8 because 1 is added to 2
Answer:
3:10.5
Step-by-step explanation:
3/2 = 1.5. Therefore, you have to multiply 2 and 7 by 1.5 to find the equivalent ratio.
Reggie lost three spaceships in level 3 of a video game he lost 30 points for each spaceship when he completed level three heat earned a bonus of 200 points by how much did his score change.
Answer:
His score change was 110
Step-by-step explanation:
Lets say he started at 0 points and lost 30 points for each spaceship thats 3 x 30 which is 90 so he's sitting at -90 points then got 200 so thats -90 + 200 = 110
Add a carnival how about ix pack of 16 ticket each he ha ued 38 of the ticket o far how many ticket doe he have left
Add a carnival how about ix pack of 16 ticket each he ha ued 38 of the ticket o far 106 many ticket doe he have left.
What is Carnival?A event known as carnival takes place over a few days, typically in February or March, soon before Lent. Carnival is an occasion to indulge in these pleasures for the last time since traditionally, many people fast throughout Lent, giving up meat, sweets, or other meals and beverages.
Carnival is often marked by large-scale activities that include the public, such as parades, open-air gatherings, and other shows that incorporate aspects of the circus. People might put aside their normal uniqueness and feel a stronger feeling of communal solidarity when wearing elaborate costumes and masks.
Now, find out how many tickets he bought in total -
he bought 9 packs with 16 tickets, so inside each pack:
9 x 16 = 144
= 144 - 38
= 106
So, he has 106 tickets left.
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assume x and y are functions of t. evaluate for the following. y^3=2x^3 10 x=5,3,4
To evaluate the given expressions, substitute the values of 'x' into the equation y^3 = 2x^3 and solve for 'y'.
For x = 5:
y^3 = 2(5)^3
y^3 = 250
Taking the cube root of both sides, we get:
y = ∛250
For x = 3:
y^3 = 2(3)^3
y^3 = 54
Taking the cube root of both sides, we get:
y = ∛54
For x = 4:
y^3 = 2(4)^3
y^3 = 128
Taking the cube root of both sides, we get:
y = ∛128
Therefore, the values of 'y' corresponding to the given values of 'x' are:
For x = 5: y ≈ ∛250
For x = 3: y ≈ ∛54
For x = 4: y ≈ ∛128
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suppose after graduating from msba, you work for a survey research company. in a typical survey, you mail questionnaires to 150 companies. some of these companies might decide not to respond. assume that the nonresponse rate is 45%; that is, each company's probability of not responding, independently of the others, is 0.45.
The expected number of companies that might not respond is 67.5.
Based on the given information, we can model the nonresponse rate using a binomial distribution. Let's define the following variables:
n = Number of questionnaires mailed = 150
p = Probability of not responding = 0.45
To determine the number of companies that might not respond, we can calculate the probability of different scenarios using the binomial distribution formula:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
Where:
X represents the number of companies that do not respond.
k represents the number of companies that do not respond.
C(n, k) is the binomial coefficient, calculated as C(n, k) = n! / (k! * (n - k)!)
To find the probability of a specific number of companies not responding, we substitute the values of n, p, and k into the formula.
For example, to find the probability that exactly 70 companies do not respond, we can calculate:
P(X = 70) = C(150, 70) * 0.45^70 * (1 - 0.45)^(150 - 70)
To find the expected number of nonresponses, we can use the formula:
E(X) = n * p
In this case:
E(X) = 150 * 0.45
So the expected number of companies that might not respond is 67.5.
Note: The binomial distribution assumes independent and identically distributed trials, so it is important to ensure that the assumption holds in the given scenario.
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the answer choices are 39, 51, 70.5, 78 please help! i’ll give brainliest
Answer: 51 degrees
Step-by-step explanation:
If K = {(x, y ) | x - y = 5}, is Set K a function?
Yes, Set K is a function.
To determine if Set K is a function, we need to check if for every x-value in Set K, there is a unique corresponding y-value.
Set K is defined as {(x, y) | x - y = 5}.
This means that any pair (x, y) in Set K must satisfy the equation x - y = 5.
To test if it is a function, we can consider two scenarios:
If we fix a value for x, is there a unique value for y that satisfies the equation x - y = 5?
If we fix a value for x, say x = 7, we can substitute it into the equation and solve for y:
7 - y = 5
-y = 5 - 7
-y = -2
y = 2
In this case, there is a unique value of y (y = 2) that satisfies the equation x - y = 5 when x = 7.
If we fix a value for y, is there a unique value for x that satisfies the equation x - y = 5?
If we fix a value for y, say y = 3, we can substitute it into the equation and solve for x:
x - 3 = 5
x = 5 + 3
x = 8
In this case, there is a unique value of x (x = 8) that satisfies the equation x - y = 5 when y = 3.
Since for every x-value in Set K, there is a unique corresponding y-value, and vice versa, we can conclude that Set K is indeed a function.
Therefore, Set K is a function.
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Please help me. I am confused.
Answer:
Step-by-step explanation:
100% - 75% = 25% = 0.25
x² = 16² × 0.25 = 64
x = 8
A researcher selects a sample and administers a treatment to the individuals in the sample. if the sample is used for a hypothesis test, what does the null hypothesis (h0) say about the treatment?
The null hypothesis (H0) says about the treatment is that it does not affect the scores.
What is hypothesis testing?Hypothesis testing is the statistical method that uses the data from a sample to conclude a population parameter or a population distribution.
There are two types of hypothesis testing. They are the null hypothesis and the alternative hypothesis.
If the obtained value is less than the threshold value then the null hypothesis is accepted and the alternative hypothesis is rejected.If the obtained value is greater than the threshold value then the null hypothesis is rejected and the alternative hypothesis is accepted.What is a null hypothesis?The null hypothesis says that there is no difference between the sample means of the two groups.This is a statement about a population parameter.Where the possibilities are the same.It is given that,
A researcher selects a sample and administers a treatment to the individuals in the sample.
A hypothesis test is conducted on the sample.
So, the null hypothesis (H0) says about the treatment is that it does not affect the score obtained.
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a student takes a true-false test that has 14 questions and guesses randomly at each answer. let x be the number of questions answered correctly. find p(5) group of answer choices 0.0001 0.0611 0.1833 0.1222
The probability to answer 5 questions correctly from 14 true or false questions is 0.1222
The given situation represents a binomial experiment, where there are only two possible outcomes for each trial: success (answering correctly) and failure (answering incorrectly). To find the probability of a particular number of successes, we use the binomial probability formula:
P(x)= nCx × p^x × q^(n-x)
Where, n is the total number of trials, p is the probability of success on each trial, q is the probability of failure on each trial (1-p), and x is the number of successes desired.
n = 14 (total number of questions)
p = 1/2 (probability of answering correctly when guessing randomly), and q = 1/2 (probability of answering incorrectly when guessing randomly).
To find P(5), we substitute these values in the formula
P(5) = 14C5 * (1/2)^5 * (1/2)^9= 2002 * (1/32) * (1/512)= 2002 / 16384≈ 0.1222
Therefore, the answer is option D, 0.1222.
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Please answer with explanation
Answer:
y = 2x + 1
Step-by-step explanation:
Line is passing through the points (-3, - 5) and (4, 9)
Slope of the line (m) \( =\frac{-5-9}{-3-4}=\frac{-14}{-7}=2\)
Equation of line in given as:
\(y - 9 = 2(x - 4) \\ \\ y - 9 = 2x - 8 \\ \\ y = 2x - 8 + 9 \\ \\ y = 2x + 1\)