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.

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