Check each ordered pair to see if it is a solution to 3x + 2y ≥ 6.

(0, 3)

(4, 2)

(-1, 3)

Plug, plug, plug; chug, chug, chug. In, out, and get it done.

3(0) + 2(3) ≥ 6?

0 + 6 ≥ 6

The inequality allows just a little bit of equality, so it squeaks on through. This is a solution to the equation.

3(4) + 2(2) ≥ 6?

12 + 4 ≥ 6

16 ≥ 6

Yes, this is true. This ordered pair is a solution.

3(-1) + 2(3) ≥ 6

-3 + 6 ≥ 6

3 ≥ 6

No, that doesn't work. If 3 were greater than 6, everything would fall apart. Dogs and cats living together, mass hysteria. We won't allow it.

Graph y > -3x + 1.

We'll be graphing the boundary line y = -3x + 1 with a dotted line, because a ">" is used.

Now what about our shading? Maybe we'll use (5, -7) as our test point. Nah, no way; test (0, 0) instead.

0 > -3(0) + 1?

0 > 1

This ordered pair is not a solution, so shade the half that (0, 0) is not in.

Write an equation for this graph:

We need the slope of our boundary line. We have the y-intercept, b = 6, so let's find the slope using the points (0, 6) and (1, 2).

m = -4

That gives us y = -4x + 6. But wait; don't write that down as the answer. That's almost as wrong as saying that 3 is greater than 6. Look again at our graph; it's an inequality, and a strict one at that.

How do we tell if we should have a ">" or a "<"? More plugging and chugging. Pick any point on the shaded side of the graph. We can't use (0, 0) this time, so let's go with (2, 2). Check it:

2 ? -4(2) + 6

2 ? -2

Well, 2 is greater than -2, or 2 > -2. That means our full inequality is:

y > -4x + 6