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

Step by step

The question

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

① y > x + 2 and ② y < x − 1

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 false

Is 0 more than 2?

No, false.

So we shade the other side, away from (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 = −1.

Start on the y-axis at −1.

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 − 1

0 < −1 false

Is 0 less than −1?

No, false.

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

3 Where both are shaded

The two shaded parts never cover the same place.

No point works in both.

So there is no solution.

Nothing is shaded twice: no solution.

Let's look back.

First: graph ①.

Then: graph ②.

Last: where both are shaded.

Answer