# How do you graph y ≤ -2x+6 and x>1?

Aug 4, 2015

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

#### Explanation:

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

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

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

Step 2. Plot $x = 1$

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

Step 3. Shade the area that satisfies both conditions.

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

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.