Graph y >= -2x + 1 and y <= x + 3 Step by Step

Step by step

The question

Question: graph y ≥ −2x + 1 and y ≤ x + 3.

① y ≥ −2x + 1 and ② y ≤ x + 3

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 = −2.

Go right 1,

then down 2.

Dot.

Join the dots: solid.

Which side?

We test one point: (0, 0).

Put x = 0 and y = 0 into ①.

① 0 ≥ −2(0) + 1

0 ≥ 1 false

Is 0 more than or equal to 1?

No, false.

So we shade the other side, away from (0, 0), in red.

2 Graph ②

②: The sign has "or equal to".

So the line is solid.

② ≤ → solid line

b = 3.

Start on the y-axis at 3.

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 ②.

② 0 ≤ 0 + 3

0 ≤ 3 true

Is 0 less than or equal to 3?

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 ≥ −2(1) + 1

1 ≥ −1 true

Now ②.

② 1 ≤ 1 + 3

1 ≤ 4 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