How do you graph the inequality #y>x+12#?

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Answer 1 · 2018-06-19T12:12:01

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#

#y = 0 + 12#

#y = 12# or #(0, 12)#

For: #x = -12#

#y = -12 + 12#

#y = 0# or #(-12, 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-12)^2-0.25)((x+12)^2+y^2-0.25)(y-x-12)=0 [-30, 30, -15, 15]}

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

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

graph{(y-x-12) > 0 [-30, 30, -15, 15]}