Question

Find the equation of the line whose graph is sketched below.

Short answer

Equation of the line is $4x+3y+12=0$.

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 $\frac{\text{rise}}{\text{run}}$.

$\begin{array}{l}m=\frac{\text{rise}}{\text{run}}\\ =-\frac{4}{3}\end{array}$

Step 3. Write the equation in a general form.

Use the slope-intercept form to write the equation of the line$m=-\frac{4}{3}$ and

$b=-4$:

$\begin{array}{l}y=mx+b\\ y=-\frac{4}{3}x+\left(-4\right)\\ y=-\frac{4}{3}x-4\end{array}$

role="math" localid="1644237019643" $\begin{array}{l}3\cdot y=3\cdot \left(-\frac{4}{3}x\right)-3\cdot 4\\ 3y=-4x-12\\ 4x+3y+12=0\end{array}$