Question

How do you graph the inequality `y<=-5x-5`?

Answer 1

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 = (-5 xx 0) - 5`

`y = 0 - 5`

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

For: `x = -1`

`y = (-5 xx -1) - 5`

`y = 5 - 5`

`y = 0` or `(-1, 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)^2-0.075)((x+1)^2+y^2-0.075)(5x+y+5)=0 [-15, 15, -7.5, 7.55]}

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

graph{(5x+y+5) <= 0 [-15, 15, -7.5, 7.55]}