# How do you graph y+5 \le -4x+10?

Mar 22, 2018

See below.

#### Explanation:

$y + 5 \le - 4 x + 10$

Subtract 5 from both sides.

$y \le - 4 x + 5$

Now, consider the limiting case where $y = - 4 x + 5$

This is the straight line with graph below.

graph{-4x+5 [-16.02, 16.02, -8.01, 8.01]}

It should now be clear that our inequality may be represented by all points where $y$ is less than or equal to that line.

This is the area to the left of the line and the line itself. Shown below.

graph{y<=-4x+5 [-16.02, 16.02, -8.01, 8.01]}