Henry is starting a t-shirt printing business and plans on selling each shirt for $30, with his cost being $8 per shirt. The equipment will cost $1200.
Henry orders 600 shirts and determines that the profit for his new business is modeled by the function P = 22x - 1200. What is the domain of this function in this context?
{0 ≤ x ≤ 600}
{0 ≥ x ≥ 600}
{-1,200 ≤ x ≤ 2,000}
all real numbers
Answers
The domain of the function here is {0 ≤ x ≤ 600}. The first option is the right answer.
What is the domain of a function?The domain of a function is the set of all input values (or independent variables) for which the function is defined and produces a valid output (or dependent variable). It is the set of values that can be plugged into a function and yield a valid result.
The domain of this function in this context is {0 ≤ x ≤ 600}.
This is because x represents the number of t-shirts Henry sells and he has ordered 600 shirts. So, he can only sell a non-negative number of shirts (x ≥ 0) and a maximum of 600 shirts (x ≤ 600). Any values outside this range are not meaningful in this context, hence they are not part of the domain.
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Related Questions
10x5+4to the power of 2+(5+30 divided by 10 how to solve
Answers
The value of the expression is 74.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
To solve this expression, we need to follow the order of operations, which is a set of rules that dictate the order in which mathematical operations should be performed. The order of operations is: Parentheses
Exponents and Multiplication and Division (performed left to right)
Addition and Subtraction (performed left to right)
Using this order, we can evaluate the expression as follows:
10 × 5 + 16+ (5 + 30 ÷ 10)
= 50 + 16 + (5 + 3)
= 50 + 16 + 8
= 74
Therefore, the value of the expression is 74.
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A football team lost 5 yards on each of 3 plays. Explain how you could use a number line to find the team's change in field positive after the 3 plays. Then find and interpret the change in position.
Answers
The total spots moved, after the 3 plays is 15 spots to the left.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given that the football team lost 5 yards on each 3 plays.
Assume that a number line to be able to see how far in the field did they lost in 3 games.
Therefore,
1 : 5 (1 game is to 5 yards)
3 : 15 (3 games is to 15 yards )
After the first play, we would move to the left on the line 5 spots (to simulate 5 yards lost) and then make a dot to show your new position.
The total spots moved, after the 3 plays is 15 spots to the left.
Hence, All they lost 15 yards in 3 games.
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A cell phone plan cost thirty dollars for each line. does the situation represent a function
Answers
When the cell phone plan cost thirty dollars for each line, the function is C = 30x.
How to illustrate the information?It should be noted that a function is used to show the relationship that exists between the variables that are given.
In this situation, the cell phone plan cost thirty dollars for each line.
Let each line be represented by x.
Therefore, the cost for the number of likes will be:
C = 30 × x
C = 30x
Therefore, the function is illustrated.
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can SOMEBODY HELP ME WITH THIS LESSON I NEED HELP ASAP !!
Answers
Answer:
what's your question? I'm here to help if I can.
Is the airplane’s altitude a function of time?
Answers
Answer:
No, because each output of altitude has more than one input of time. ... No, because the altitude is constant between 60 minutes and 130 minutes
Step-by-step explanation:
look at the graph
Answer: C
Step-by-step explanation:
#4) Find the unit tangent vector T(t) at the point with the given value of the parameter t.
r(t) = <4te?t, 8 arctan t, 8et> t = 0
#5) Find r(t) if r'(t) = t5 i + et j + 5te5t k and r(0) = i + j + k.
#6) Find f?'(3), where f(t) = u(t) · v(t), u(3) = <1, 2, ?1>, u'(3)=<3, 0, 9>, and v(t) =
#7) Evaluate the integral: (5 sin4 t cos t i + 3 sin t cos2 t j + 4 sin t cos t k)dt from 0 to pi/2
#8) Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.
x = e?4t cos 5t, y = e?4t sin 5t, z = e?4t; (1, 0, 1)
(x(t), y(t), z(t)) = ?
Answers
Evaluating the integral from 0 to pi/2, #4) To find the unit tangent vector T(t), we first find r'(t):
r(t) = <4te^(-t), 8 arctan t, 8et>
r'(t) = <4e^(-t) - 4te^(-t), 8/(1+t^2), 8e^t>
At t = 0, we have r'(0) = <4, 8, 8>, so the magnitude of r'(0) is sqrt(4^2 + 8^2 + 8^2) = sqrt(144) = 12.
Thus, the unit tangent vector at t = 0 is T(0) = r'(0)/|r'(0)| = <4/12, 8/12, 8/12> = <1/3, 2/3, 2/3>.
#5) To find r(t), we integrate r'(t):
r'(t) = t^5 i + e^t j + 5te^5t k
Integrating each component separately, we get:
r(t) = (1/6)t^6 i + e^t j + (1/2)e^5t k
Using the initial condition r(0) = i + j + k, we get:
r(0) = (1/6)(0)^6 i + e^0 j + (1/2)e^0 k = i + j + (1/2)k
So the parametric equations for r(t) are:
x(t) = (1/6)t^6
y(t) = e^t
z(t) = (1/2)e^5t
#6) We have f(t) = u(t) · v(t), where u(t) = <1, 2, -1> and v(t) = <e^(2t), 3t^2, ln t>.
Thus, f'(t) = u'(t) · v(t) + u(t) · v'(t), where u'(t) = <3, 0, 9>.
At t = 3, we have u(3) = <1, 2, -1>, u'(3) = <3, 0, 9>, v(3) = <e^6, 9, ln 3>, and v'(3) = <2e^6, 6, 1/3>.
So, f'(3) = u'(3) · v(3) + u(3) · v'(3) = <3, 0, 9> · <e^6, 9, ln 3> + <1, 2, -1> · <2e^6, 6, 1/3>
= (3e^6 + 2e^6) + 18 + (-1/3) = 5e^6 + 53/3.
Therefore, f?'(3) = 5e^6 + 53/3.
#7) We integrate each component of the vector separately:
∫(5 sin^4 t cos t i + 3 sin t cos^2 t j + 4 sin t cos t k) dt =
(5/5)sin^5 t + (3/3)sin t cos^3 t + (4/4)sin^2 t + C
= sin^5 t + sin t cos^3 t + sin^2 t + C
Evaluating the integral from 0 to pi/2,
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The Brennan Aircraft Division of TLN Enterprises operates a large number of computerized plotting machines. For the most part, the plotting devices are used to create line drawings of complex wing airfoils and fuselage part dimensions. The engineers operating the automated plotters are called loft lines engineers. The computerized plotters consist of a minicomputer system connected to a 4- by 5-foot flat table with a series of ink pens suspended above it When a sheet of clear plastic or paper is properly placed on the table, the computer directs a series of horizontal and vertical pen movements until the desired figure is drawn. The plotting machines are highly reliable, with the exception of the four sophisticated ink pens that are built in. The pens constantly clog and jam in a raised or lowered position. When this occurs, the plotter is unusable. Currently, Brennan Aircraft replaces each pen as it fails. The service manager has, however, proposed replacing all four pens every time one fails. This should cut down the frequency of plotter failures. At present, it takes one hour to replace one pen. All four pens could be replaced in two hours. The total cost of a plotter being unusable is $50 per hour. Each pen costs $8. If only one pen is replaced each time a clog or jam occurs, the following breakdown data are thought to be valid: Hours between plotter failures if one pen is replaced during a repair Probability 10 0.05 20 0.15 30 0.15 40 0.20 50 0.20 60 0.15 70 0.10 Based on the service manager’s estimates, if all four pens are replaced each time one pen fails, the probability distribution between failures is as follows: Hours between plotter failures if four pens are replaced during a repair Probability 100 0.15 110 0.25 120 0.35 130 0.20 140 0.00 (a) Simulate Brennan Aircraft’s problem and determine the best policy. Should the firm replace one pen or all four pens on a plotter each time a failure occurs?
Answers
To determine the best policy for Brennan Aircraft's plotter pen replacement, we can simulate the problem and compare the expected costs for both scenarios: replacing one pen or replacing all four pens each time a failure occurs.
Let's calculate the expected costs for each scenario:
Replacing one pen:
We'll calculate the expected cost per hour of plotter failure by multiplying the probability of each failure duration by the corresponding cost per hour, and then summing up the results.
Expected cost per hour = Σ(Probability * Cost per hour)
Expected cost per hour = (10 * 0.05 + 20 * 0.15 + 30 * 0.15 + 40 * 0.20 + 50 * 0.20 + 60 * 0.15 + 70 * 0.10) * $50
Expected cost per hour = $39.50
Replacing all four pens:
We'll calculate the expected cost per hour using the same method as above, but using the probability distribution for the scenario of replacing all four pens.
Expected cost per hour = (100 * 0.15 + 110 * 0.25 + 120 * 0.35 + 130 * 0.20 + 140 * 0.00) * $50
Expected cost per hour = $112.50
Comparing the expected costs, we can see that replacing one pen each time a failure occurs results in a lower expected cost per hour ($39.50) compared to replacing all four pens ($112.50). Therefore, the best policy for Brennan Aircraft would be to replace one pen each time a failure occurs.
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Use Horner's algorithm to find p(4), where p(z) = 325 – 724 – 57'+z? -- 8z +2 2.
Answers
Using Horner's algorithm, it is found that p(4) = 946.
Horner's algorithm is a method used to evaluate a polynomial at a given value of x. It simplifies the process of calculating the value of the polynomial by reducing the number of calculations needed. To use Horner's algorithm to find p(4), where p(z) = 3z^5 – 7z^4 – 5z^3+z^2- 8z +2, follow these steps:
p(4) = 3(4)^5 – 7(4)^4 – 5(4)^3+(4)^2- 8(4) +2
p(4) = 3(4)^5 – 7(4)^4 – 5(4)^3+(4)^2- 8(4) +2
p(4) = 3(1024) – 7(256)– 5(64) + 16 - 32 +2
p(z) = 3072– 1792 – 320 + 16 - 30
p(z) = 1280 – 320 - 14
p(z) = 960 - 14
p(z) = 946
Therefore, p(4) = 946.
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The dimensions of a rectangular prism are 5 cm, 6m, and x cm. Its surface area is 148cm Find the other dimension
Answers
Answer: 4 cm
You take the surface area formula and substitute “x” for the width. Then it becomes a simple algebra problem.
Express the following numbers as a ratio between an internet and a natural number: 1 2/5,. 3, -3 1/4, -27, 0
Answers
So, the ratios for the given numbers are:
7/5, 3/1, -13/4, -27/1, and 0/1.
1 2/5 can be expressed as the ratio 1/1 + 2/5 = 7/5
3 can be expressed as the ratio 3/1
-3 1/4 can be expressed as the ratio -13/4
-27 can be expressed as the ratio -27/1
0 can be expressed as the ratio 0/1
An ordered pair of integers a and b, represented as a / b, is a ratio if b is not equal to 0.
A proportion is an equation that sets two ratios at the same value.
For example, if there is 1 boy and 3 girls you could write the ratio as:
1 : 3 (for every one boy there are 3 girls)1 / 4 are boys and 3 / 4 are girls0.25 are boys (by dividing 1 by 4)25% are boys (0.25 as a percentage)So, the ratios for the given numbers are:
7/5, 3/1, -13/4, -27/1, and 0/1.
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oint c is the center of the circle above. what fraction of the area of the circle is the area of the shaded regio
Answers
Fraction of the area of the circle is the area of the shaded region is 5/18.
From the figure:
The shaded region has angle = 100
In the circle the total angle is 360.
Fraction = 100/360
= 50/180
= 25/90
= 5/18
Therefore fraction of the area of the circle is the area of the shaded region is 5/18.
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question 5 options: there is no prior information about the proportion of americans who support medicare-for-all in 2019. if we want to estimate 95% confidence interval for the true proportion of americans who support medicare-for-all in 2019 with a 0.175 margin of error, how many randomly selected americans must be surveyed?
Answers
You will find that approximately 384 randomly selected Americans need to be surveyed to estimate the 95% confidence interval for the true proportion of Americans who support Medicare-for-all in 2019 with a margin of error of 0.175.
To estimate a 95% confidence interval for the true proportion of Americans who support Medicare-for-all in 2019, with a margin of error of 0.175, you need to survey a sufficient number of randomly selected Americans.
To calculate the sample size required, you can use the formula:
n = (Z^2 * p * (1-p)) / E^2
Where:
n = sample size
Z = Z-score corresponding to the desired confidence level (for 95% confidence level, Z = 1.96)
p = estimated proportion (since there is no prior information, you can assume p = 0.5 for maximum sample size)
E = margin of error (0.175 in this case)
Plugging in the values, the formula becomes:
n = (1.96^2 * 0.5 * (1-0.5)) / 0.175^2
Simplifying the equation, you will find that approximately 384 randomly selected Americans need to be surveyed to estimate the 95% confidence interval for the true proportion of Americans who support Medicare-for-all in 2019 with a margin of error of 0.175.
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kodi needs to refill the ink in his pen, so he needs to find its volume. which three-dimensional figure should he use to model the pen?
Answers
Step-by-step explanation:
Probably a cylinder would work best
volume of a cylinder = pi r^2 h
Adam borrowed $17 from his brother on Monday, and then an additional $5 on Tuesday. How much money will Adam have to pay his brother in order to be free of debt?
Answers
Answer:
$23
Step-by-step explanation:
Answer:
$23 is how much he will owe
11. Jim travelled at a speed of 18km/h for 2 hours. What was the distance covered?
Answers
Answer:
36 km/h
Step-by-step explanation:18 x 2 since every hour jim went another 18 km for two hours.
Write an integer for the situation. 15 degrees below normal
Answers
Answer:
It's -15 than normal
For 5-8, use the diagram to complete each sentence.
(diagram attached)
5. An exterior angle of the triangle is ________.
6. The remote interior angles of the triangle to the exterior angle 1 are ________ and ________.
7. The sum of the measure of angles 2 and 3 is equal to the measure of ________.
8. The sum of the measure of angles 1 and 4 is _______.
Answers
By using the diagram, each of the sentence should be completed as follows;
An exterior angle of the triangle is ∠1.The remote interior angles of the triangle to the exterior angle 1 are ∠2 and ∠3.The sum of the measure of angles 2 and 3 is equal to the measure of ∠1.The sum of the measure of angles 1 and 4 is 180°.What is the exterior angle theorem?In Mathematics, the exterior angle theorem can be defined as a theorem which states that the measure of an exterior angle in a triangle is equal in magnitude to the sum of the measures of the two remote or opposite interior angles of that triangle.
By applying the exterior angle theorem, we can reasonably infer and logically deduce that the sum of the measure of both angle 2 and angle 3 in the given triangle is equal to the measure of angle 1 (∠1);
∠2 + ∠3 = ∠1
By applying the Linear Pair Postulate to the two angles formed at a point, we have the following:
∠1 + ∠4 = 180°
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If u had powers what power would u have
Answers
Answer:
I would have psychic powers so I could have multiple powers.
Fraction: 1/11, Numerator: 1
Step-by-step explanation:
Find the coordinates of point M if S(-4, 5) is the midpoint of MP and the coordinates of Pare (-8, 8).
O (0, 2)
(6,6 1/2)
(0, -2)
O (-2, 0)
Answers
The coordinates of point M are (-6, 6.5). Option (B) is the correct answer.
We are given that S(-4, 5) is the midpoint of MP and the coordinates of P are (-8, 8). We want to find the coordinates of point M.
Since point S is the midpoint of MP, we can use the midpoint formula to find the coordinates of point M:
Midpoint formula: (xm, ym) = ((xp + xs)/2, (yp + ys)/2)
Substituting the given values, we get:
(xm, ym) = ((-8 - 4)/2, (8 + 5)/2)
(xm, ym) = (-6, 6.5)
The other points listed in the answer choices are not relevant to this problem.(option-b)
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Using the midpoint formula to solve the equations gives us the coordinates of M as (0,2).
Explanation:In mathematics, we can find the coordinates of the point M using the formula properties of a line division. Since S is the midpoint, that means it equally divides the line segment MP into two. The midpoint formula is M = [(x1+x2)/2 , (y1+y2)/2]. You have the coordinates of S(-4,5) and P(-8,8), so we can set up the following equations using the midpoint formula:
(-4+X)/2 = -8 and (5+Y)/2 = 8
Solving these equations for X and Y, we get X = 0 and Y = 2. Therefore, the coordinates of M would be (0,2), which is option O (0,2) in your given choices.
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Set up and evaluate a double integral to find the volume of the solid bounded by the graphs of the equations. z = x + y x2 + y? = 64 first octant V = dy dx =
Answers
Answer:
The volume of the solid bounded by the given equations is approximately 170.67 cubic units.
Step-by-step explanation:
To find the volume of the solid, we need to set up the double integral as follows:
V = ∫∫R (x + y) dA
where R is the region in the first octant bounded by the graph of x^2 + y^2 = 64.
Converting the equation of the boundary to polar coordinates, we have:
\(r^2 = x^2 + y^2 = 64\)
so r = 8.
The limits of integration for r are 0 to 8, and for θ are 0 to π/2, since we are only interested in the first octant.
Thus, the double integral is:
V = ∫0^(π/2) ∫0^8 (r cosθ + r sinθ) r dr dθ
\(= ∫0^(π/2) ∫0^8 r^2 cosθ dr dθ + ∫0^(π/2) ∫0^8 r^2 sinθ dr dθ\)
Evaluating each integral separately, we get:
\(V = (1/3)[r^3 cosθ]0^π/2 [0^8] + (1/3)[r^3 sinθ]0^π/2 [0^8]\)
\(= (1/3)[(8^3)(1) - (0^3)(1)] + (1/3)[(8^3)(0) - (0^3)(0)]\)
= (1/3)(512) + 0
= 170.67
Therefore, the volume of the solid bounded by the given equations is approximately 170.67 cubic units.
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The perimeter of an equilateral triangle can be represented by 6x+36. Which of the following expressions represents the length of one of the sides of the triangle?
A. 3(2x+12)
B. 2x+12
C. 6x+33
D. 3x+18
Please help quick!!
Answers
Answer:
2x + 12
Step-by-step explanation:
6x + 36 / 3 =
(6x)/3 + (36)/3 = 2x + 12
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The lowest temperature recorded in Canada was -63 degrees. The highest temperature recorded in Canada was +45 degrees. What is the difference between the temperatures?
Answers
Answer:
108 degrees difference.
Step-by-step explanation:
63+45=108
Answer:
108
Step-by-step explanation:
45--63=108
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the density of iron is 7.8 g/cm^3 and its mass is 15 g . the volume of iron rim
Answers
Answer:
Step-by-step explanation:
d=m/V
7.8=15/V
V=15/7.8
≈1.92 cm³
Help please. The question about bananas.
Answers
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Share 800 in the ratio 9:7.
Answers
Answer:
The numerator '9's share is 450 and the denominator '7's share is 350.Step-by-step explanation:
Step-1: Add the ratios:
9 + 716Step-2: Divide 800 by the sum of the ratios:
800 ÷ 16=> 50Step-3: Multiply 50 with each ratio:
9 x 50 = 4507 x 50 = 350Hence, the numerator '9's share is 450 and the denominator '7's share is 350.
Hoped this helped.
\(BrainiacUser1357\)
Sharing 800 in the ratio of 9:7 gives us two shares as 450 and 350 respectively.
What do we mean by a ratio?A ratio is a pair of numbers, say x and y, written as x:y, said as x is to y, and used as the fraction x/y, where y ≠ 0.
How do we solve the given question?We are asked to share 800 in the ratio of 9:7.
To do this, we denote the share as 9x and 7x respectively.
Sum of the shares = 9x + 7x = 16x.
This sum needs to be equal to the total we are asked to share, that is, 800.
∴ 16x = 800
Dividing both sides by 16, we get
16x/16 = 800/16
or, x = 50.
To determine each share, we multiply the value of x = 50.
∴ Shares are:
9x = 9 * 50 = 450
7x = 7 * 50 = 350
So sharing 800 in the ratio of 9:7 gives us two shares as 450 and 350 respectively.
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Let f be the function defined by f(x)=xlnx for x>0. On what open interval is f decreasing?
Answers
The function f(x) = xlnx is decreasing on the open interval (0, e^-1).
To find the interval on which the function f(x) = xlnx is decreasing, we need to find the intervals where the first derivative f'(x) is negative.
Using the product rule of differentiation, we can find the first derivative of f(x) as
f'(x) = x × (1/x) + ln(x) × 1 = 1 + ln(x)
Now, we need to find the values of x where f'(x) < 0
1 + ln(x) < 0
ln(x) < -1
x < e^-1
Therefore, f(x) is decreasing on the interval (0, e^-1).
Note that we exclude x = 0 from the interval because the function is not defined for x ≤ 0.
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Let z = Equals 38 (cos(pi/8) + I sine (cos(pi//8) ) and w = 2 (cos(pi/16) + I sine (pi/16) ) What is the product of zw?
Answers
The product of the terms zw is 76{ cos(3π/16)+i sin (3π/16) }.
Given that,
The equation are z = 38[cos(π/8)+i sin(π/8)] and w = 2[cos(π/16)+i sin(π/16)]
We have to find the product of the zw.
Whatis product?Finding the product of two or more numbers in math is done through multiplication. It is a fundamental mathematical operation that is frequently applied in everyday situations. When combining groups of similar sizes, we use multiplication.
Take the equation,
zw= (38[cos(π/8)+i sin(π/8)])×(2[cos(π/16)+i sin(π/16)])
zw=(38×2){Cos(π/8+π/16)+i sin(π/8+π/16)}
zw= 76{ cos(3π/16)+i sin (3π/16) }
Therefore, the product of the terms zw is 76{ cos(3π/16)+i sin (3π/16) }.
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A florist has 56 and 70 carnations to make a table centerpiece he wants to put an equal number of roses and carnations into each centerpiece
Answers
The maximum number of Centerpieces that could be made by the florist with the given number of roses and carnations is 14.
To Determine the maximum number of centerpieces, we have to find the Least Common Multiple of the given number of Roses and Carnations.
The given values are:
Roses = 56
Carnations = 70
Taking all the factors of both numbers,
we can write them as,
Roses = 1 * 2 * 4 * 7
Carnations = 1 * 2 * 5 * 7
Then, the common factors would be,
= 1 * 2 * 7
= 14
From this we can conclude that the maximum number of centerpieces of roses and carnations that can be made by the florist is 14
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What is the best approximation of the solution to the
system to the nearest integer values?
O (-6, 1)
0 (0,-7)
0 (1,-6)
O (2,7)
Answers
Answer: Choice C. (1, -6)
Explanation: The two lines cross at around this location. The solution point is on both lines at the same time.
Please help!!!!!!!!!!!
Answers
Answer: F= 4
Step-by-step explanation:
rise over run!
-4 (from the run in the slope) plus 8 (your x axis) is 4