Question

use the intercepts to graph -7x-2y=-21

Answer 1

The Slope-Intercept form of the equation of a line is:

$y=mx+b$

Where "m" is the slope of the line and "b" is the y-intercept.

Given the following equation:

$-7x-2y=-21​$

You can write it in Slope-Intercept form by solving for "y":

$\begin{gathered} -2y=7x-21​ \\ \\ y=\frac{7}{-2}x-\frac{21}{-2} \\ \\ y=-3.5x+10.5 \end{gathered}$

You can identify that the y-intercept is:

$b=10.5$

By definition, the line intersects the x-axis when:

$y=0$

Then, substituting this value into the equation and solving for "x", you can find the x-intercept:

$\begin{gathered} 0=-3.5x+10.5 \\ -10.5=-3.5x \\ \\ \frac{-10.5}{-3.5}=x \\ \\ x=3 \end{gathered}$

Knowing the x-intercept and the y-intercept, you can graph the line.

The answer is: