Chapter 8.5, Problem 22WE

To determine

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

Answer to Problem 22WE

The equation in slope intercept form of the given lineis $y=-\frac{x}{3}+\frac{10}{3}$ .

Explanation of Solution

Given information:

The points through the line passes is $\left(-2,4\right),\left(4,2\right)$ .

Calculation:

The slope of the line is,

  $\begin{array}{c}m=\frac{y_2-y_2}{x_2-x_1}\\ =\frac{2-4}{4+2}\\ =\frac{-2}{6}\\ =-\frac{1}{3}\end{array}$

The slope intercept form is,

  $y=mx+c$

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

Substitute the values in above equation.

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

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

  $\begin{array}{c}4=-\frac{1}{3}\left(-2\right)+c\\ 4=\frac{2}{3}+c\\ c=4-\frac{2}{3}\\ =\frac{10}{3}\end{array}$

Substitute the value in equation (1).

  $y=-\frac{x}{3}+\frac{10}{3}$