How do you graph the inequality #x - y > 2#?

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Answer 1 · 2018-05-29T13:04:04

See a solution process below:

First, solve for two points as an equation instead of an inequality to find the boundary line for the inequality.

For: #x = 0#

#0 - y = 2#

#-y = 2#

#-y * color(red)(-1) = 2 * color(red)(-1)#

#y = -2# or #(0, -2)#

For: #y = 0#

#x - 0 = 2#

#x = 2# or #(2, 0)#

We can now graph the two points on the coordinate plane and draw a line through the points to mark the boundary of the inequality.

graph{(x^2+(y+2)^2-0.035)((x-2)^2+y^2-0.035)(x-y-2)=0 [-10, 10, -5, 5]}

Now, we can shade the right side of the line.

We also need to change the boundary line to a dashed line because the inequality operator does not contain an "or equal to" clause.

graph{(x-y-2) > 0 [-10, 10, -5, 5]}