Chapter 3.4, Problem 34PPS

To determine

To find: Slope intercept form of given graph .

Answer to Problem 34PPS

  $y=\left(\frac{8}{7}\right)x-2$

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 $\left(0,-2\right)$

So,

Y-intercept $c=-2$

Line also passed through the point $\left(7,6\right)$

Therefore

  $\begin{array}{l}\left(x_1,y_1\right)=\left(0,-2\right)\\ \left(x_2,y_2\right)=\left(7,6\right)\\ Slope=\frac{y_2-y_1}{x_2-x_1}\\ \Rightarrow m=\frac{6-\left(-2\right)}{7-0}\\ \Rightarrow m=\frac{6+2}{7}\\ \Rightarrow m=\frac{8}{7}\end{array}$

Slope intercept form of given graph is

  $\begin{array}{l}y=mx+c\\ \Rightarrow y=\left(\frac{8}{7}\right)x-2\end{array}$