Question

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

Short answer

Slope-intercept of the line in the graph is$y=\frac{3}{4}x+2$.

Step-by-step solution

Step 1. Given information.

The garph as shown below is given.

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

It can be seen that y-intercept is $\left(0,2\right)$and the line passes through $\left(4,5\right)$.

Find slope as follows.

$$\begin{gathered} m=\frac{rise}{run} \\ m=\frac{5-2}{4-0} \\ m=\frac{3}{4} \end{gathered}$$

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

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

Substitute the values as follows.

$$\begin{gathered} y=mx+b \\ y=\frac{3}{4}x+2 \end{gathered}$$

Therefore, slope-intercept from of the line is$y=\frac{3}{4}x+2$.