How do you graph the inequality #y<x-3#?

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Answer 1 · 2018-06-15T19:36:34

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 - 3#

#y = -3# or #(0, -3)#

For: #x = 4#

#y = 4 - 3#

#y = 1# or #(4, 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^2+(y+3)^2-0.035)((x-4)^2+(y-1)^2-0.035)(y-x+3)=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{(y-x+3) < 0 [-10, 10, -5, 5]}