Chapter 8.5, Problem 27WE

To determine

To find: The equation in slope intercept form of the given line.

Answer to Problem 27WE

The equation in slope intercept form of the given lineis $y=-\frac{3}{4}x-\frac{3}{2}$ .

Explanation of Solution

Given information:

The points through the line passes is $\left(-2,0\right),\left(2,-3\right)$ .

Calculation:

The slope of the line is,

  $\begin{array}{c}m=\frac{y_2-y_2}{x_2-x_1}\\ =\frac{-3-0}{2+2}\\ =-\frac{3}{4}\end{array}$

The slope intercept form is,

  $y=mx+c$

Here, the slope is $m$ and $y$ intercept is $c$ .

Substitute the values in above equation.

  $y=-\frac{3}{4}x+c$................(1)

Substitute the values of point through which the line is passing in above equation.

  $\begin{array}{c}-3=-\frac{3}{4}\left(2\right)+c\\ -3=-\frac{3}{2}+c\\ c=-\frac{3}{2}\end{array}$

Substitute the value in equation (1).

  $y=-\frac{3}{4}x-\frac{3}{2}$