Graph y = 2x + 1 and y = 2x - 3

Step by step

The question

Question: solve by graphing y = 2x + 1 and y = 2x − 3.

The answer is a point that is on both lines.

So we draw both lines and see where they meet.

1 Graph line ①

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.

In ①, 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 with a straight line.

2 Graph line ②

In ②, b = −3.

Start on the y-axis at −3.

m = 2.

As a fraction: 2/1.

Go right 1,

then up 2.

Dot.

Join the dots with a straight line.

3 Where they meet

Both have slope 2, but they start at different places: 1 and −3.

So they are parallel: they never meet.

So there is no solution.

Let's look back.

First: graph line ①.

Then: graph line ②.

Last: where they meet.