Jimena Mcconnell

2023-02-21

How to use the intercepts to graph the equation $x-4y=-8$?

Caiden Mitchell

Where the line crosses the y-axis is known as the y-intercept, and x = 0. The x-intercept is where the line crosses the x-axis and y = 0. This will give you two points on your line.
Determine the y-intercept, where x = 0.
$0-4y=-8$
$-4y=-8$
Divide both sides by -4.
$y=2$
Where y = 0, find the x-intercept.
$x-0y=-8$
$x=-8$
So now you have two points on your line with the y-intercept and x-intercept: (0, 2), representing $\left({x}_{1},{y}_{1}\right)$; and (-8, 0), representing $\left({x}_{2},{y}_{2}\right)$.
Now that you have two points on the line, you can determine the slope, m, using the equation $m$ = $\frac{\left({y}_{2}-{y}_{1}\right)}{\left({x}_{2}-{x}_{1}\right)}$.
For this line:
$m$ = $\frac{\left(0-2\right)}{\left(-8-0\right)}=-\frac{2}{-8}=\frac{1}{4}$
The following is a graph of the line showing the y-intercept of 2 and the x-intercept of -8.

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