Find three solutions for the linear equation 4x −3y = 1, and plot the solutions as points on a coordinate plane.

Answer:

(1, 1), (2, 2.333) and (3, 3.666).

Step-by-step explanation:

To find solutions for this equation, we can just choose values for x and then calculate the values of y.

So, for x = 1, we have:

4*1 - 3y = 1

3y = 3

y = 1

For x = 2, we have:

4*2 - 3y = 1

3y = 7

y = 2.333

For x = 3, we have:

4*3 - 3y = 1

3y = 11

y = 3.666

The points we need to plot is (1, 1), (2, 2.333) and (3, 3.666).

Check the image attached for the plot.

Three solutions for the linear equation are: (0, -0.333), (1,1) and (3, 3.667).

The graph is given at the end of this answer.

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The equation is:

\(4x - 3y = 1\)

In slope-intercept formula, we have that:

\(3y = 4x - 1\)

\(y = \frac{4}{3}x - \frac{1}{3}\)

Thus, the solutions are given by the following pairs of points: \((x, \frac{4}{3}x - \frac{1}{3})\)

-----------------------------

For x = 0, we have that \(y = \frac{4}{3}(0) - \frac{1}{3} = -\frac{1}{3} = -0.333\), thus, one solution is (0, -0.333).

For x = 1, we have that \(y = \frac{4}{3}(1) - \frac{1}{3} = \frac{3}{3} = 1\), thus, one solution is (1,1).

For x = 3, we have that \(y = \frac{4}{3}(3) - \frac{1}{3} = \frac{11}{3} = 3.667\), thus, one solution is (3, 3.667).

These solutions are labeled on the graph given at the end of this answer.

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