How do you graph x ≥ -1, y ≥ -2, and 2x + y ≤ 6?

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Answer 1 · 2015-08-03T21:18:27

Plot each graph separately and then shade the area that satisfies all three inequalities.

Your equations are #x ≥ -1#, #y ≥ -2#, and #2x + y ≤ 6#.

Step 1. Plot #x=-1#.

Use a solid line because your condition is not a strict inequality.

Graph 1

Step 2. Plot #y = -2#

Again, use a solid line.

Graph 2

Step 3. Plot #2x + y = 6#.

Rearrange the equation to #y=6-2x#

Graph 3

Step 4. Shade the area that satisfies all three conditions.

Graph 4

Check: Test a point in the coloured region.

Try (#0,0#).

#x≥-1#
#0≥-1#
∴ TRUE

#y≥-2#
#-0≥-2#
∴ TRUE

#2x + y ≤ 6#.
#2(0)+0≤6#
#0+0≤6#
#0<=6#
∴ TRUE

The point (#0,0#) satisfies all three conditions.