Graph y >= 2x Step by Step | Graphing inequalities

Step by step

The question

Question: graph y ≥ 2x.

y ≥ 2x

The answer is not one point.

It is every point that makes this true.

That is a whole part of the grid.

answer = all the points that work

1 Draw the line

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

y = 2x

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.

≥ → solid 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 = 0.

Start on the y-axis at 0.

m = 2.

As a fraction: 2/1.

Go right 1,

then up 2.

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: (1, 0).

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

Put x = 1 and y = 0 in.

0 ≥ 2(1)

0 ≥ 2 false

Is 0 more than or equal to 2?

No, that is false.

So (1, 0) is not an answer.

3 Shade

So we shade the other side, away from (1, 0).

Every point there is an answer.

4 Check

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

Put x = −1 and y = −1 in.

−1 ≥ 2(−1)

−1 ≥ −2 true

True!

So the shading is right.

Let's look back.

First: draw the line.

Then: test a point.

Then: shade.

Last: check.

Answer