Chapter 3.4, Problem 36PPS

To determine

To find: Slope intercept form of given graph .

Answer to Problem 36PPS

  $y=\left(\frac{1}{4}\right)x-4$

Explanation of Solution

Slope intercept form of a line is

  $y=mx+c$

  $m=slope$

  $c=$ Y-intercept.

From given graph we can say that

Line cuts Y-axis at $\left(0,-4\right)$

So,

Y-intercept $c=-4$

Line also passes through the point $\left(8,-2\right)$

Therefore

  $\begin{array}{l}\left(x_1,y_1\right)=\left(0,-4\right)\\ \left(x_2,y_2\right)=\left(8,-2\right)\\ Slope=\frac{y_2-y_1}{x_2-x_1}\\ \Rightarrow m=\frac{\left(-2\right)-\left(-4\right)}{8-0}\\ \Rightarrow m=\frac{-2+4}{8}\\ \Rightarrow m=\frac{2}{8}\\ \Rightarrow m=\frac{1}{4}\end{array}$

Slope intercept form of given graph is

  $\begin{array}{l}y=mx+c\\ \Rightarrow y=\left(\frac{1}{4}\right)x-4\end{array}$