Question

Write an equation in slope-intercept form for each graph shown.

Short answer

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

Step-by-step solution

Step 1. Write the slope-intercept form of a line and intercept form of the line.

The equation of line in slope-intercept form is:

$y=mx+b$

Where is the slope of the line and $b$is the $y$-intercept of the line.

The equation of line in intercept form is:

$\frac{x}{a}+\frac{y}{b}=1$

Where $a$and $b$are the $x$- and $y$-intercepts of the line.

Step 2. Write the equation of the given graph in intercept form.

From the given graph, it can be noticed that the $x$- and $y$-intercepts of the given graph are $-3$and 2 respectively.

Therefore, the values of $a$and $b$are $-3$and 2 respectively.

Therefore, the equation of the line in intercept form is:

$\begin{array}{c}\frac{x}{a}+\frac{y}{b}=1\\ \frac{x}{-3}+\frac{y}{2}=1\end{array}$

Step 3. Write the equation of the given graph in slope-intercept form.

Rewrite the equation $\frac{x}{-3}+\frac{y}{2}=1$in the slope-intercept form to find the equation of the given graph in slope-intercept form.

Therefore, it is obtained that:

$\begin{array}{c}\frac{x}{-3}+\frac{y}{2}=1\\ \frac{-x}{3}+\frac{y}{2}=1\\ \frac{y}{2}=\frac{x}{3}+1\\ y=2(\frac{x}{3}+1)\\ y=\frac{2}{3}x+2\end{array}$

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