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

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Answer 1 · 2018-03-22T05:17:46

See below.

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

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]}

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