How do you graph the inequality #y <-2x+5#?

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Answer 1 · 2018-06-17T13:21:23

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 = 1#

#y = (-2 * 1) + 5#

#y = -2 + 5#

#y = 3# or #(1, 3)#

For: #x = 2#

#y = (-2 * 2) + 5#

#y = -4 + 5#

#y = 1# or #(2, 1)#

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-1)^2+(y-3)^2-0.035)((x-2)^2+(y-1)^2-0.035)(y + 2x-5)=0 [-10, 10, -5, 5]}

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

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

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