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$y=\frac{-3}{2}x-1$.

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 $\left(0,-1\right)$and the line passes through the point $\left(2,-4\right)$as well.

Find slope as follows.

$$\begin{gathered} m=\frac{rise}{run} \\ m=\frac{-4-\left(-1\right)}{2-0} \\ m=\frac{-3}{2} \end{gathered}$$

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

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

Substitute the values.

$$\begin{gathered} y=mx+b \\ y=\frac{-3}{2}x-1 \end{gathered}$$

Therefore, slope-intercept form of the line in the graph is$y=\frac{-3}{2}x-1$.