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 $\left(0 , 5\right)$

For: $x = - 2$

$y = - 2 + 5$

$y = 3$ Or $\left(- 2 , 3\right)$

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]}