Step by step
The question
Question: graph y = −2x + 3.
1 Read m and b
b is the number on its own: 3.
The line crosses the y-axis at 3.
That point is called the y-intercept.
m is the number in front of x: −2.
It is the slope.
As a fraction: −2/1.
The bottom is the run: right 1.
The top is the rise: down 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 3.
Put a dot.
3 Use the slope
From the dot, go right 1,
then down 2.
Put a dot.
Again: right 1,
down 2.
Dot.
We can also go back: left 1,
up 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 = 1 and x = 2.
Put x = 1 in.
We get y = 1.
The point (1, 1) is on our line.
Now x = 2 in.
We get y = −1.
The point (2, −1) 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.