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 $\mathit{y}\mathbf{=}\mathbf{-}\frac{\mathbf{1}}{\mathbf{5}}\mathit{x}\mathbf{+}\mathbf{1}$.

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 5 and 1 respectively.

Therefore, the values of $a$and $b$are 5 and 1 respectively.

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

$\begin{array}{c}\frac{x}{a}+\frac{y}{b}=1\\ \frac{x}{5}+\frac{y}{1}=1\end{array}$

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

Rewrite the equation $\frac{x}{5}+\frac{y}{1}=1$in the slope-intercept form to find the equation of the given graph in slope-intercept form.

Therefore, it is obtained that:

$\begin{array}{c}\frac{x}{5}+\frac{y}{1}=1\\ \frac{x}{5}+y=1\\ y=-\frac{x}{5}+1\\ y=\frac{-1}{5}x+1\end{array}$

Therefore, the equation of the given graph in slope-intercept form is $y=-\frac{1}{5}x+1$.