Graph y < x + 2 and y > -x Step by Step

Step by step

The question

Question: graph y < x + 2 and y > −x.

① y < x + 2 and ② y > −x

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 is less than, with no "or equal to".

So the line is dashed.

① < → dashed line

b = 2.

Start on the y-axis at 2.

m = 1.

Go right 1,

then up 1.

Dot.

Join the dots: dashed.

Which side?

We test one point: (0, 0).

Put x = 0 and y = 0 into ①.

① 0 < 0 + 2

0 < 2 true

Is 0 less than 2?

Yes, true.

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

2 Graph ②

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

So the line is dashed.

② > → dashed line

b = 0.

Start on the y-axis at 0.

m = −1.

Go right 1,

then down 1.

Dot.

Join the dots: dashed.

Which side?

We test one point: (1, 0).

(0, 0) is on the line, so we take (1, 0).

Put x = 1 and y = 0 into ②.

② 0 > −1 true

Is 0 more than −1?

Yes, true.

So we shade the side with (1, 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, 2).

Put it into ①.

① 2 < 1 + 2

2 < 3 true

Now ②.

② 2 > −1 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