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$y=2x+1$.

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 $\left(1,3\right),\left(0,1\right).$

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 from of the line equation that passes through the point $\left(x_1,y_1\right)$with slope $m$isrole="math" localid="1646132732448" $y-y_1=m\left(x-x_1\right)$.

Step 3. Find the equation of the line.

Here, $\left(x_1,y_1\right)=\left(0,1\right),\left(x_2,y_2\right)=\left(1,3\right).$

Find the slope.

$$\begin{gathered} m=\frac{3-1}{1-0} \\ m=2 \end{gathered}$$

Substitute $m=2,x_1=0,y_1=1$in $y-y_1=m\left(x-x_1\right)$.

$\begin{array}{rcl}y-1& =& 2\left(x-0\right)\\ y-1& =& 2x\\ y& =& 2x+1\end{array}$

The line equation is $\begin{array}{rcl}y& =& 2x+1\end{array}$.