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=(7)/(-2)x-(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 \\ \\ (-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: