Question

Write an equation in slope-intercept form for each graph.

Short answer

The equation of the graph in slope-intercept form is$y=\frac{2}{3}x+\frac{1}{3}$.

Step-by-step solution

Step 1. Given Information.

From the given graph, the line passes through $\left(4,3\right)$ and $\left(-2,-1\right)$. The equation of the line in slope-intercept form is to be determined.

Step 2. Calculation.

The equation of a line in slope-intercept form is y=mx+b, where m is the slope of the line and b is the y-intercept.

The slope of a line passing through two points is given by:

$\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{-1-3}{-2-4}\\ m=\frac{-4}{-6}\\ m=\frac{2}{3}\end{array}$

The equation of a line with slope m and passing through a point is given by:

$\begin{array}{l}y-y_1=m\left(x-x_1\right)\\ y-3=\frac{2}{3}\left(x-4\right)\\ y-3=\frac{2}{3}x-\frac{8}{3}\\ y=\frac{2}{3}x-\frac{8}{3}+3\\ y=\frac{2}{3}x+\frac{1}{3}\end{array}$

Step 3. Conclusion.

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