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.

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