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

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Answer 1 · 2015-08-03T21:18:27

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

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

Step 1. Plot $x=-1$ .

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

Graph 1

Step 2. Plot $y = -2$

Again, use a solid line.

Graph 2

Step 3. Plot $2x + y = 6$ .

Rearrange the equation to $y=6-2x$

Graph 3

Step 4. Shade the area that satisfies all three conditions.

Graph 4

Check: Test a point in the coloured region.

Try ( $0,0$ ).

$x≥-1$
$0≥-1$
∴ TRUE

$y≥-2$
$-0≥-2$
∴ TRUE

$2x + y ≤ 6$ .
$2(0)+0≤6$
$0+0≤6$
$0<=6$
∴ TRUE

The point ( $0,0$ ) satisfies all three conditions.