Question

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

Short answer

Equation of the line is $3x-2y-6=0$.

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

$\begin{array}{l}m=\frac{\text{rise}}{\text{run}}\\ =\frac{-3}{-2}\\ =\frac{3}{2}\end{array}$

Step 3. Write the equation in a general form.

Use the slope-intercept form to write the equation of the line$m=\frac{3}{2}$ and

role="math" $b=-3$:

$\begin{array}{l}y=mx+b\\ y=\frac{3}{2}x+\left(-3\right)\\ y=\frac{3}{2}x-3\end{array}$

$\begin{array}{l}2\cdot y=2\cdot \left(\frac{3}{2}x-3\right)\\ 2y=3x-6\\ 2y-3x+6=0\\ 3x-2y-6=0\end{array}$