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]}