Chapter 3.4, Problem 72PFA

To determine

To find: Slope intercept form of given graph .

Answer to Problem 72PFA

  $y=\left(\frac{-2}{3}\right)x+4$

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 passed through the point $\left(6,0\right)$

Therefore

  $\begin{array}{l}\left(x_1,y_1\right)=\left(0,4\right)\\ \left(x_2,y_2\right)=\left(6,0\right)\\ Slope=\frac{y_2-y_1}{x_2-x_1}\\ \Rightarrow m=\frac{0-4}{6-0}\\ \Rightarrow m=\frac{-4}{6}\\ \Rightarrow m=\frac{-2}{3}\end{array}$

Slope intercept form of given graph is

  $\begin{array}{l}y=mx+c\\ \Rightarrow y=\left(\frac{-2}{3}\right)x+4\end{array}$