Question

How do you graph the inequality `6x + 4y ≤ 24`?

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`

`(6 * 0) + 4y = 24`

`0 + 4y = 24`

`4y = 24`

`(4y)/color(red)(4) = 24/color(red)(4)`

`y = 6` or `(0, 6)`

For: `y = 0`

`6x + (4 * 0) = 24`

`6x + 0 = 24`

`6x = 24`

`(6x)/color(red)(6) = 24/color(red)(6)`

`x = 4` or `(4, 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-6)^2-0.125)((x-4)^2+y^2-0.125)(6x+4y-24)=0 [-20, 20, -10, 10]}

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

graph{(6x+4y-24) <= 0 [-20, 20, -10, 10]}