Step by step
The question
Question: solve by graphing y = 3x − 2 and y = x.
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 = −2.
Start on the y-axis at −2.
m = 3.
As a fraction: 3/1.
Go right 1,
then up 3.
Dot.
Join the dots with a straight line.
2 Graph line ②
In ②, b = 0.
Start on the y-axis at 0.
m = 1.
As a fraction: 1/1.
To stay on the grid, we go the other way.
Both moves turn round, so the slope stays the same.
Go left 1,
then down 1.
Dot.
Join the dots with a straight line.
3 Where they meet
The lines meet at one point.
Go straight down to the x-axis: x = 1.
Go straight across to the y-axis: y = 1.
So x = 1 and y = 1, both at the same time: the point (1, 1).
4 Check in both
Let's check: put x = 1 and y = 1 into both equations.
First ①.
We get 1.
That is y.
It works.
Now ②.
We get 1.
That is y.
It works.
(1, 1) is on both lines.
So the answer is right!
Let's look back.
First: graph line ①.
Then: graph line ②.
Then: where they meet.
Last: check in both.