Q. 4 - Precalculus Enhanced with Graphing Utilities

Question

Find the equation of the line containing the points (-1, 4) and (2, -2). Express your answer in slope–intercept form and graph the line. 

Step-by-Step Solution

Answer

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Step 1. Given information.

Find the equation of the line containing the points (-1, 4) and (2, -2). Express your answer in slope–intercept form and graph the line. 

Step 2. Definition.

The equation of line ( in slope - intercept form) is given by:

$y=mx+b; m\ne 0$

The slope of the graph is m and y- intercept is b . The average rate of change is equal to slope:

$m=\frac{y_2-y_1}{x_2-x_1}$

Step 3. Equation of line.

Slope:

$$\begin{gathered} A=\left(x_1,y_1\right)=\left(-1,4\right) \\ B=\left(x_2,y_2\right)=\left(2,-2\right) \end{gathered}$$

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{-2-4}{2-(-1)}=\frac{-6}{3}=-2$

So, the slope is $m=-2$.

Y - intercept:

The point $(2,-2)$ is on the, because we want to find b , put the coordinates of the points inside the equation:

$$\begin{gathered} y=mx+b \\ -2=-2·2+b \\ -2=-4+b \\ b=-2+4 \\ b=2 \end{gathered}$$

So the equation of line is:

$y=-2x+2$

Step 4. Graph the equation of line.