Question

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

Short answer

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

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

$\begin{array}{l}m=\frac{\text{rise}}{\text{run}}\\ =\frac{-4}{4}\\ =-1\end{array}$

Step 3. Write the equation in a general form.

Use the slope-intercept form to write the equation of the line$m=-1$ and

$b=4$:

$\begin{array}{l}y=mx+b\\ y=\left(-1\right)x+4\\ y=-x+4\\ x+y-4=0\end{array}$