Question

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

Answer 1

See below.

Explanation:

`y+5<=-4x+10`

Subtract 5 from both sides.

`y<=-4x+5`

Now, consider the limiting case where `y=-4x+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]}