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

Aug 3, 2015

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

#### Explanation:

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".

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

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

Step 3. Shade the area that satisfies both conditions.

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

Check Test a point in the coloured region.

Try ($0 , - 2$).

$y < x - 1$
$- 2 < 0 - 1$
$- 2 < - 1$
∴ TRUE

$y \le 2 x + 1$
$- 2 \le 2 \left(0\right) + 1$
$- 2 = 0 + 1$
$- 2 \le 1$
∴ TRUE

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