# How do you graph the inequality y<= 2x + 2?

Aug 5, 2016

See the explanation.

#### Explanation:

Suppose $x = 3$ then $2 x + 2 = 8$

So the inequality of $y \le 2 x + 2$ for $x = 3$ is saying:

$y$ can be 8 and/or all the values less than 8

As $y$ can actually assume the value of 8 the line is solid.

Suppose the equation had been $y < 2 x + 2$ in this instance if $x = 3$ then $y$ is not permitted to assume the value of 8 but it is allowed to assume any of the values less than 8. In this case the line would be dotted.

Aug 5, 2016

Draw the line $y = 2 x + 2$ that passes through (-1, 0 and (0, 2). Shade the region below. For any (x, y) on and beneath this line $y \le 2 x + 2$.

#### Explanation:

Draw the line $y = 2 x + 2$. It passes through (-1, 0 and (0, 2). Shade

the region below this line.

For any point (x, y) on and beneath this linem $y \le 2 x + 2$.