Question

Find the equation of the line whose graph is sketched below.(Lesson 1.10)

Short answer

Equation of the line is $2x-y+4=0$.

Step-by-step solution

Step 1. Definition of slope-intercept form.

Slope-intercept is the equation of a straight line in the form $y=mx+b$where m is the slope of the line and b is its y-intercept.

Step 2. Find the slope of the given line.

Use any two points on the line and interpret the slope as $\frac{\text{rise}}{\text{run}}$.

So, the slope is

localid="1644235986182" $\begin{array}{l}m=\frac{\text{rise}}{\text{run}}\\ =\frac{-4}{-2}\\ =2\end{array}$

Step 3. Write the equation in a general form.

Use the slope-intercept form to write the equation of the line$m=2$ and

$b=4$:

$\begin{array}{l}y=mx+b\\ y=2x+4\\ y=2x+4\end{array}$

$\begin{array}{l}-2x+y-4=0\\ 2x-y+4=0\end{array}$