Question

How do you graph the inequality `4x+3y> -12`?

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`

`(4 * 0) + 3y = -12`

`0 + 3y = -12`

`3y = -12`

`(3y)/color(red)(3) = -12/color(red)(3)`

`y = -4` or `(0, -4)`

For: `y = 0`

`4x + (3 * 0) = -12`

`4x + 0 = -12`

`4x = -12`

`(4x)/color(red)(4) = -12/color(red)(4)`

`x = -3` or `(-3, 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+4)^2-0.05)((x+3)^2+y^2-0.05)(4x+3y+12)=0 [-15, 15, -7.5, 7.5]}

Now, we can shade the right side of the line. We also have to make the boundary line a dashed line because the inequality operator does not contain an "or equal to" clause so the boundary line is not included in the solution set.

graph{(4x+3y+12) > 0 [-15, 15, -7.5, 7.5]}