Question

How do you graph the inequality `x+8y>16`?

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 + 8y = 16`

`8y = 16`

`(8y)/color(red)(8) = 16/color(red)(8)`

`y = 2` or `(0, 2)`

For: `x = 8`

`8 + 8y = 16`

`-color(red)(8) + 8 + 8y = -color(red)(8) + 16`

`0 + 8y = 8`

`8y = 8`

`(8y)/color(red)(8) = 8/color(red)(8)`

`y = 1` or `(8, 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.

graph{(x^2+(y-2)^2-0.025)((x-8)^2+(y-1)^2-0.025)(x+8y-16)=0 [-10, 10, -5, 5]}

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

The boundary line will change to a dashed line because the inequality operator does not contain an "or equal to" clause.

graph{(x+8y-16) > 0 [-10, 10, -5, 5]}