How do you graph y>=-x+7 on the coordinate plane?

Dec 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: $x = 0$

$y = 0 + 7$

$y = 7$

$y = 7$ or $\left(0 , 7\right)$

For: $x = 2$

$y = - 2 + 7$

$y = 5$ or $\left(2 , 5\right)$

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-7)^2-0.125)((x-2)^2+(y-5)^2-0.125)(y + x - 7)=0 [-20, 20, -10, 10]}

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

graph{(y + x - 7)>=0 [-20, 20, -10, 10]}