Chapter 3.4, Problem 67PFA

To determine

To find: Slope intercept form of given graph .

Answer to Problem 67PFA

  $y=3x+2$

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 $\left(2,8\right)$

Therefore

  $\begin{array}{l}\left(x_1,y_1\right)=\left(0,2\right)\\ \left(x_2,y_2\right)=\left(2,8\right)\\ Slope=\frac{y_2-y_1}{x_2-x_1}\\ \Rightarrow m=\frac{8-2}{2-0}\\ \Rightarrow m=\frac{6}{2}\\ \Rightarrow m=3\end{array}$

Slope intercept form of given graph is

  $\begin{array}{l}y=mx+c\\ \Rightarrow y=3x+2\end{array}$