Chapter 8.5, Problem 20WE

To determine

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

Answer to Problem 20WE

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

Explanation of Solution

Given information:

The points through the line passes is $\left(-3,4\right),\left(3,-4\right)$ .

Calculation:

The slope of the line is,

  $\begin{array}{c}m=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{-4-4}{3-\left(-3\right)}\\ =\frac{-8}{6}\\ =-\frac{4}{3}\end{array}$

The slope intercept form is,

  $y=mx+c$

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

Substitute the values in above equation.

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

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

  $\begin{array}{l}4=-\frac{4}{3}\left(-3\right)+c\\ 4=\frac{12}{3}+c\\ 4=4+c\\ c=0\end{array}$

Substitute the value in equation (1).

  $y=-\frac{4}{3}x$