Question

Find the equation of the line shown in each graph and write the equation in slope-intercept form.

Short answer

Slope-intercept form of the line is$y=\frac{-4}{3}x+3$.

Step-by-step solution

Step 1. Given information.

The graph as shown below is given.

Step 2. Find the slope and y-intercept of the line.

It can be seen that y-intercept is $\left(0,3\right)$and the line passes through $\left(3,-1\right)$.

Find slope as follows.

$$\begin{gathered} m=\frac{rise}{run} \\ m=\frac{3-\left(-1\right)}{0-3} \\ m=\frac{-4}{3} \end{gathered}$$

Step 3. Substitute the values in slope-intercept form.

Slope intercept form is $y=mx+b$.

Substitute the values.

$$\begin{gathered} y=mx+b \\ y=\frac{-4}{3}x+3 \end{gathered}$$

Therefore, slope-intercept form of the line is$y=\frac{-4}{3}x+3$.