Jimena Mcconnell

2023-02-21

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

Caiden Mitchell

Beginner2023-02-22Added 3 answers

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 $({x}_{1},{y}_{1})$; and (-8, 0), representing $({x}_{2},{y}_{2})$.

Now that you have two points on the line, you can determine the slope, m, using the equation $m$ = $\frac{({y}_{2}-{y}_{1})}{({x}_{2}-{x}_{1})}$.

For this line:

$m$ = $\frac{(0-2)}{(-8-0)}=-\frac{2}{-8}=\frac{1}{4}$

The following is a graph of the line showing the y-intercept of 2 and the x-intercept of -8.

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 $({x}_{1},{y}_{1})$; and (-8, 0), representing $({x}_{2},{y}_{2})$.

Now that you have two points on the line, you can determine the slope, m, using the equation $m$ = $\frac{({y}_{2}-{y}_{1})}{({x}_{2}-{x}_{1})}$.

For this line:

$m$ = $\frac{(0-2)}{(-8-0)}=-\frac{2}{-8}=\frac{1}{4}$

The following is a graph of the line showing the y-intercept of 2 and the x-intercept of -8.