Question

How do you graph `4x-2y>20`?

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) - 2y = 20`

`0 - 2y = 20`

`-2y = 20`

`(-2y)/color(red)(-2) = 20/color(red)(-)`

`y = -10` or `(0, -10)`

For: `y = 0`

`4x - (2 * 0) = 20`

`4x - 0 = 20`

`4x = 20`

`(4x)/color(red)(4) = 20/color(red)(4)`

`x = 5` or `(5, 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.

graph{(x^2+(y+10)^2-0.25)((x-5)^2+y^2-0.25)(4x-2y-20)=0 [-30, 30, -15, 15]}

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

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

graph{(4x-2y-20) > 0 [-30, 30, -15, 15]}