Graph y > 2x - 1 Easy

The question

Question: graph y > 2x − 1.

The answer is not one point.

It is every point that makes this true.

That is a whole part of the grid.

1 Draw the line

First we draw the line where both sides are equal: y = 2x − 1.

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

So points on the line are not answers.

We draw it dashed, like the open circle on a number line.

Draw the grid.

The x-axis goes across.

The y-axis goes up and down.

They meet at 0.

That point is called the origin.

b = −1.

Start on the y-axis at −1.

m = 2.

As a fraction: 2/1.

Go right 1,

then up 2.

Dot.

Join the dots: dashed.

2 Test a point

The line cuts the grid in two sides.

One side is the answer.

We test one point: (0, 0).

Zeros are easy to work with.

Put x = 0 and y = 0 in.

Is 0 more than −1?

Yes, that is true.

So (0, 0) is an answer.

3 Shade

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

Every point there is an answer.

4 Check

Let's check with a point in the shaded part: (−2, −1).

Put x = −2 and y = −1 in.

True!

So the shading is right.

Let's look back.

First: draw the line.

Then: test a point.

Then: shade.

Last: check.

▶ Watch it solved

Graph y <= -x + 3 Medium

The question

Question: graph y ≤ −x + 3.

The answer is not one point.

It is every point that makes this true.

That is a whole part of the grid.

1 Draw the line

First we draw the line where both sides are equal: y = −x + 3.

The sign has "or equal to".

So points on the line are answers too.

We draw it solid, like the filled circle on a number line.

Draw the grid.

The x-axis goes across.

The y-axis goes up and down.

They meet at 0.

That point is called the origin.

b = 3.

Start on the y-axis at 3.

m = −1.

As a fraction: −1/1.

Go right 1,

then down 1.

Dot.

Join the dots: solid.

2 Test a point

The line cuts the grid in two sides.

One side is the answer.

We test one point: (0, 0).

Zeros are easy to work with.

Put x = 0 and y = 0 in.

Is 0 less than or equal to 3?

Yes, that is true.

So (0, 0) is an answer.

3 Shade

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

Every point there is an answer.

4 Check

Let's check with a point in the shaded part: (−2, −1).

Put x = −2 and y = −1 in.

True!

So the shading is right.

Let's look back.

First: draw the line.

Then: test a point.

Then: shade.

Last: check.

▶ Watch it solved

Graph x + 2y < 4 Harder

The question

Question: graph x + 2y < 4.

The answer is not one point.

It is every point that makes this true.

That is a whole part of the grid.

1 Draw the line

First we draw the line where both sides are equal: x + 2y = 4.

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

So points on the line are not answers.

We draw it dashed, like the open circle on a number line.

On the x-axis, y = 0.

Put 0 in place of y.

2 times 0 is 0.

Adding 0 changes nothing.

So x = 4.

On the y-axis, x = 0.

Put 0 in place of x.

0 plus 2y is just 2y.

2y means 2 times y.

We want just y.

To remove times 2, we divide by 2.

We do it on both sides, so they stay equal.

2 divided by 2 is 1.

So just y is left.

4 divided by 2 is 2.

So y = 2.

So the line crosses the axes at (4, 0) and (0, 2).

Draw the grid.

The x-axis goes across.

The y-axis goes up and down.

They meet at 0.

That point is called the origin.

Put the two crossing points on the grid,

and join them: dashed.

2 Test a point

The line cuts the grid in two sides.

One side is the answer.

We test one point: (0, 0).

Zeros are easy to work with.

Put x = 0 and y = 0 in.

Is 0 less than 4?

Yes, that is true.

So (0, 0) is an answer.

3 Shade

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

Every point there is an answer.

4 Check

Let's check with a point in the shaded part: (−2, −1).

Put x = −2 and y = −1 in.

True!

So the shading is right.

Let's look back.

First: draw the line.

Then: test a point.

Then: shade.

Last: check.

▶ Watch it solved