How do you graph the inequality #y<1/2x+2#?

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Answer 1 · 2018-07-18T13:47:49

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 = (1/2 xx 0) + 2#

#y = 0 + 2#

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

For: #x = 2#

#y = (1/2 xx 2) + 2#

#y = 2/2 + 2#

#y = 1 + 2#

#y = 3# or #(2, 3)#

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)^2-0.04)((x-2)^2+(y-3)^2-0.04)(-0.5x+y-2)=0 [-10, 10, -5, 5]}

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

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

graph{(-0.5x+y-2) < 0 [-10, 10, -5, 5]}