Chapter 9.2, Problem 8MRE

To determine

To find: Theequation in the slope-intercept form.

Answer to Problem 8MRE

The equation in the slope-intercept form is $y=\frac{2}{3}x+2$ .

Explanation of Solution

Given information:

The slope of the line is $\frac{2}{3}$ and passes through point $\left(6,6\right)$ .

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 $b$ .

The y intercept of the line is calculated as,

  $\begin{array}{l}y=mx+b\\ 6=\left(\frac{2}{3}\right)\left(6\right)+b\\ 6=4+b\\ b=2\end{array}$

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

  $\begin{array}{l}y=mx+b\\ y=\frac{2}{3}x+2\end{array}$

Thus, the equation in the slope-intercept form is $y=\frac{2}{3}x+2$ .