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

Feb 6, 2015

The y-intercept is where the line crosses the y-axis, 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.

$0 - 4 y = - 8$
$- 4 y = - 8$
Divide both sides by -4.
$y = 2$

Determine the x-intercept, where y = 0.

$x - 0 y = - 8$
$x = - 8$

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.