Question

How do you graph `-4x+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`

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

`0 + y = -6`

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

For: `x = 2`

`(-4 * 2) + y = -6`

`-8 + y = -6`

`-8 + color(red)(8) + y = -6 + color(red)(8)`

`0 + y = 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+6)^2-0.08)((x-2)^2+(y-2)^2-0.08)(-4x+y+6)=0 [-20, 20, -10, 10]}

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

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

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