Step by step
The question
Question: solve by graphing y = x + 2 and 2y − 2x = 4.
The answer is a point that is on both lines.
So we draw both lines and see where they meet.
1 Crossing points of ②
On the x-axis, y = 0.
Put 0 in place of y.
2 times 0 is 0.
0 minus 2x is −2x.
−2x means −2 times x.
We want just x.
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 x is left.
Plus over minus is minus.
4 divided by −2 is −2.
So x = −2.
On the y-axis, x = 0.
Put 0 in place of x.
2 times 0 is 0.
Taking away 0 changes nothing.
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 line ② crosses the axes at (−2, 0) and (0, 2).
2 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 = 2.
Start on the y-axis at 2.
m = 1.
As a fraction: 1/1.
Go right 1,
then up 1.
Dot.
Join the dots with a straight line.
3 Graph line ②
Put the two crossing points on the grid,
and join them.
4 Where they meet
Both equations make the same line.
They meet everywhere.
So every point on the line works.
Let's look back.
First: crossing points of ②.
Then: graph line ①.
Then: graph line ②.
Last: where they meet.