How do you graph #x-5<=y#?

1 Answer
Nov 30, 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#

#0 - 5 = y#

#-5 = y#

#y = -5# or #(0, -5)#

For: #x = 5#

#5 - 5 = y#

#0 = y#

#y = 0# or #(5, 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.
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-5)^2+y^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]}