Question

How do you graph the inequality `-5x+2y<-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`

`(-5 * 0) + 2y = -6`

`0 + 2y = -6`

`2y = -6`

`(2y)/color(red)(2) = -6/color(red)(2)`

`y = -3` or `(0, -3)`

For: `x = 2`

`(-5 * 2) + 2y = -6`

`-10 + 2y = -6`

`color(red)(10) + 10 + 2y = color(red)(10) + -6`

`0 + 2y = 4`

#2y = 4

`(2y)/color(red)(2) = 4/color(red)(2)`

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

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+3)^2-0.125)((x-2)^2+(y-2)^2-0.125)(-5x+2y+6)=0 [-20, 20, -10, 10]}

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

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

graph{(-5x+2y+6) > 0 [-20, 20, -10, 10]}