Question

In the following exercises, find the equation of the line shown in each graph. Write the equation in slope-intercept form.

Short answer

The slope-intercept form of the equation of the line in the shown graph is$y=\frac{3}{4}x-2$.

Step-by-step solution

Step 1. Given information: 

The provided graph of a line equation is:

Step 2. Evaluate/formulas  

From the graph, take two points that lie on the line are say $\left(0,-2\right),\left(4,1\right)$.

The slope between two points $\left(x_1,y_1\right),\left(x_2,y_2\right)$is $m=\frac{y_2-y_1}{x_2-x_1}$.

The point-slope form of the line equation that passes through the point $\left(x_1,y_1\right)$ with slope$m$is$y-y_1=m\left(x-x_1\right)$.

Step 3. Find the equation of the line.

Here, $\left(x_1,y_1\right)=\left(0,-2\right),\left(x_2,y_2\right)=\left(4,1\right)$.

Find the slope.

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

Substitute $m=\frac{3}{4},x_1=0,y_1=-2$in $y-y_1=m\left(x-x_1\right)$.

$\begin{array}{rcl}y-\left(-2\right)& =& \frac{3}{4}\left(x-0\right)\\ y+2& =& \frac{3}{4}x\\ y& =& \frac{3}{4}x-2\end{array}$

The line equation is$y=\frac{3}{4}x-2$.