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 $\mathit{y}\mathbf{=}\mathbf{-}\mathbf{2}\mathit{x}\mathbf{+}\mathbf{3}$.

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$m$ 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 $1.5$and 3 respectively.

Therefore, the values of $a$and $b$are$1.5$ and 3 respectively.

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

$\begin{array}{c}\frac{x}{a}+\frac{y}{b}=1\\ \frac{x}{1.5}+\frac{y}{3}=1\end{array}$

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

Rewrite the equation $\frac{x}{1.5}+\frac{y}{3}=1$in the slope-intercept form to find the equation of the given graph in slope-intercept form.

Therefore, it is obtained that:

$\begin{array}{c}\frac{x}{1.5}+\frac{y}{3}=1\\ \frac{y}{3}=-\frac{x}{1.5}+1\\ y=3(\frac{-x}{1.5}+1)\\ y=\frac{-3x}{1.5}+3\\ y=-2x+3\end{array}$

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