How do you graph #y<x-1 # and #y<=2x+1#?

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Answer 1 · 2015-08-03T20:07:23

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

Your equations are #y < x−1# and #y≤2x+1#

Step 1. Plot #y = x-1#.

Use a solid line because your condition is "less than", not “less than or equal to".

Graph 1

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

Use a dashed line because your condition is "less than or equal to".

Graph 2

Step 3. Shade the area that satisfies both conditions.

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

Graph 3

Check Test a point in the coloured region.

Try (#0,-2#).

#y < x-1#
#-2<0-1#
#-2<-1#
∴ TRUE

#y<= 2x+1#
#-2<=2(0)+1#
#-2=0+1#
#-2<=1#
∴ TRUE

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