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

Sep 26, 2017

Refer to the explanation.

#### Explanation:

Graph:

$y + 2 \le - \frac{2}{3} \left(x - 6\right)$

First convert the inequality into slope-intercept form:

$y = m x + b$,

where:

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

Expand the right side.

$y + 2 \le - \frac{2}{3} x - \left(- \frac{2}{3} \times 6\right)$

Simplify.

$y + 2 \le - \frac{2}{3} x + \frac{12}{3}$

Simplify.

$y + 2 \le - \frac{2}{3} x + 4$

Subtract $2$ from both sides.

$y \le - \frac{2}{3} x + 4 - 2$

Simplify.

$y \le - \frac{2}{3} x + 2$

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

$x = 0 ,$$y = 2$ $\leftarrow$ Point: $\left(0 , 2\right)$

$x = 3 ,$$y = 0$ $\leftarrow$ Point: $\left(3 , 0\right)$

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]}