Graph y >= x - 1 and y < -2x + 4 Step by Step

Step by step

The question

Question: graph y ≥ x − 1 and y < −2x + 4.

① y ≥ x − 1 and ② y < −2x + 4

We shade the answer of each one.

Where both are shaded, both are true.

answer = the part shaded twice

1 Graph ①

Draw the grid.

①: The sign has "or equal to".

So the line is solid.

① ≥ → solid line

b = −1.

Start on the y-axis at −1.

m = 1.

Go right 1,

then up 1.

Dot.

Join the dots: solid.

Which side?

We test one point: (0, 0).

Put x = 0 and y = 0 into ①.

① 0 ≥ 0 − 1

0 ≥ −1 true

Is 0 more than or equal to −1?

Yes, true.

So we shade the side with (0, 0), in red.

2 Graph ②

②: The sign is less than, with no "or equal to".

So the line is dashed.

② < → dashed line

b = 4.

Start on the y-axis at 4.

m = −2.

Go right 1,

then down 2.

Dot.

Join the dots: dashed.

Which side?

We test one point: (0, 0).

Put x = 0 and y = 0 into ②.

② 0 < −2(0) + 4

0 < 4 true

Is 0 less than 4?

Yes, true.

So we shade the side with (0, 0), in blue.

3 Where both are shaded

This part is shaded twice.

It is the answer.

Careful!

The answer is not everything we shaded.

Only the part shaded twice works in both.

Careful: not every shaded part ✗

4 Check

Let's check with a point in the purple part: (−1, −1).

Put it into ①.

① −1 ≥ (−1) − 1

−1 ≥ −2 true

Now ②.

② −1 < −2(−1) + 4

−1 < 6 true

True in both!

So the answer is right.

Let's look back.

First: graph ①.

Then: graph ②.

Then: where both are shaded.

Last: check.

Answer