Chapter 11.6, Problem 38SR

To determine

To find: Theequation in slope-intercept form for the given graph.

Answer to Problem 38SR

The equation in slope-intercept form for the given graph is $y=-\frac{5}{3}x+\frac{29}{3}$ .

Explanation of Solution

Given information:

The given graph is,

  

Concept used:

The standard equation for the linear function cab be written as,

  $y=mx+b$

Here, the slope of the graph is $m$ and the $y$ -intercept is $b$ .

Theslope of the line is calculated as,

  $\begin{array}{c}m=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{-2-3}{7-4}\\ =\frac{-5}{3}\end{array}$

The $y$ -intercept of the line is calculated as,

  $\begin{array}{l}y=mx+b\\ 3=\frac{-5}{3}\left(4\right)+b\\ b=\frac{29}{3}\end{array}$

The equation in the slope-intercept form is obtained as,

  $\begin{array}{l}y=mx+b\\ y=-\frac{5}{3}x+\frac{29}{3}\end{array}$

Thus, the equation in slope-intercept form for the given graph is $y=-\frac{5}{3}x+\frac{29}{3}$ .