Question

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

`0 + 5y = -5`

`5y = -5`

`(5y)/color(red)(5) = -5/color(red)(5)`

`y = -1` or `(0, -1)`

For: `y = 0`

`x + (5 * 0) = -5`

`x + 0 = -5`

`x = -5` 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+1)^2-0.125)((x+5)^2+y^2-0.125)(x+5y+5)=0 [-20, 20, -10, 10]}

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

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