Question

How do you graph the inequality `8x+y<=6`?

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`

`(8 * 0) + y = 6`

`0 + y = 6`

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

For: `x = 2`

`(8 * 2) + y = 6`

`16 + y = 6`

`-color(red)(16) + 16 + y = -color(red)(16) + 6`

`0 + y = -10`

`y = -10` `(2, -10)`

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)^2-0.25)((x-2)^2+(y+10)^2-0.25)(8x+y-6)=0 [-30, 30, -15, 15]}

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

graph{(8x+y-6) <= 0 [-30, 30, -15, 15]}