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

1 Answer
Meave60
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 - 4y = -8#
#-4y = -8#
Divide both sides by -4.
#y = 2#

Determine the x-intercept, where y = 0.

#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# = #((y_2-y_1))/((x_2-x_1))#.

For this line:

#m# = #((0-2))/((-8-0)) = -2/-8 = 1/4#

The following is a graph of the line showing the y-intercept of 2 and the x-intercept of -8.
http://www.wolframalpha.com/input/?i=what+is+the+graph+of+x-4y%3D-8

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