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

Step by step

The question

Question: graph y > x − 2 and y < x + 3.

① y > x − 2 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 is more 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 more than −2?

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 = 3.

Start on the y-axis at 3.

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 ②.

② 0 < 0 + 3

0 < 3 true

Is 0 less than 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 > (−1) − 2

−1 > −3 true

Now ②.

② −1 < (−1) + 3

−1 < 2 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