Step by step
The question
Question: graph y = (2/3)x − 1.
1 Read m and b
b is the number on its own: −1.
The line crosses the y-axis at −1.
That point is called the y-intercept.
m is the number in front of x: 2/3.
It is the slope.
The bottom is the run: right 3.
The top is the rise: up 2.
2 Start at b
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.
Start on the y-axis at −1.
Put a dot.
3 Use the slope
From the dot, go right 3,
then up 2.
Put a dot.
Again: right 3,
up 2.
Dot.
We can also go back: left 3,
down 2.
Dot.
4 Draw the line
Join the dots with a straight line.
It keeps going both ways.
5 Check
Let's check with a table.
We pick x = 3 and x = 6.
Put x = 3 in.
We get y = 1.
The point (3, 1) is on our line.
Now x = 6 in.
We get y = 3.
The point (6, 3) is on our line.
Both points are on the line.
So the graph is right!
Let's look back.
First: read m and b.
Then: start at b.
Then: use the slope.
Then: draw the line.
Last: check.