Question

How do you graph `x+6y<=-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: `y = 0`

`x + (6 * 0) = -5`

`x + 0 = -5`

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

For: `y = -1`

`x + (6 * -1) = -5`

`x - 6 = -5`

`x - 6 + color(red)(6) = -5 + color(red)(6)`

`x - 0 = 1`

`x = 1` or `(1, -1)`

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+5)^2+y^2-0.125)((x-1)^2+(y+1)^2-0.125)(x+6y+5)=0 [-20, 20, -10, 10]}

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

graph{(x+6y+5) <= 0 [-20, 20, -10, 10]}