How do you graph the inequality #y>= x+5 #?

1 Answer
Nov 20, 2017

See a solution process below:

Explanation:

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 + 5#

#y = 5# Or #(0, 5)#

For: #x = -2#

#y = -2 + 5#

#y = 3# Or #(-2, 3)#

We can now plot the two points on the coordinate plane and draw a line through the points to mark the boundary of the inequality.
The boundary line will be solid because the inequality operator contains an "or equal to" clause.

graph{(x^2+(y-5)^2-0.125)((x+2)^2+(y-3)^2-0.125)(y-x-5)=0 [-20, 20, -10, 10]}

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

graph{(y-x-5) >= 0 [-20, 20, -10, 10]}