Question

How do you graph the inequality `y + 2<= -2/3(x - 6)`?

Answer 1

Refer to the explanation.

Explanation:

Graph:

`y+2<=-2/3(x-6)`

First convert the inequality into slope-intercept form:

`y=mx+b`,

where:

`m` is the slope, and `b` is the y-intercept (value of `y` when `x=0)`.

Expand the right side.

`y+2<=-2/3x-(-2/3xx6)`

Simplify.

`y+2<=-2/3x+12/3`

Simplify.

`y+2<=-2/3x+4`

Subtract `2` from both sides.

`y<=-2/3x+4-2`

Simplify.

`y<=-2/3x+2`

Determine two points on the line, starting with the y-intercept.

`x=0,` `y=2` `larr` Point: `(0,2)`

`x=3,` `y=0` `larr` Point: `(3,0)`

Plot the points on the graph and draw a straight solid line through them to indicate it is part of the graph. Then shade in the area below the line to represent the inequality.

graph{y<=-2/3x+2 [-10, 10, -5, 5]}