How do you graph #y ≤ -2x+6# and #x>1#?

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Answer 1 · 2015-08-04T16:16:44

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

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

Step 1. Plot #y =-2x+6#.

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

Graph 1

Step 2. Plot #x=1#

Use a dashed line because your condition is a strict inequality.

Graph 2

Step 3. Shade the area that satisfies both conditions.

Shade the area that is to the right of #x=1# and below #y =-2x+6#.

Graph 3

Check: Test a point in the coloured region.

Try (#2,0#).

#y ≤-2x+6#
#0≤ -2(2)+6#
#0≤-4+6#
#0≤2#
∴ TRUE

#x>1#
#2>1#
∴ TRUE

The point (#2,0#) satisfies both conditions.