Question

Find the equation of the line shown in the graph.

Short answer

The equation is$y=\frac{4}{3}x-5$.

Step-by-step solution

Step 1. Find y-intercept from the graph 

We can see that graph crosses$y-$axis at $(0,-5)$.

So the$y-$intercept is $(0,b)=(0,-5)$.

Another point on the line is$(3,-1)$.

Step 2. Find slope by counting rise and run

Slope is:

$$\begin{gathered} m=\frac{rise}{run} \\ m=\frac{4}{3} \end{gathered}$$

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

The slope-intercept form is:

$$\begin{gathered} y=mx+b \\ y=\frac{4}{3}x+(-5) \\ y=\frac{4}{3}x-5 \end{gathered}$$

The equation of the line is$y=\frac{4}{3}x-5$.