Worked examples
The question
Question: graph y = 2x + 1.
y = 2x + 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.
b = 1 → start at 1
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: up 2.
m = 2 = 21 → right 1, 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 1,
then up 2.
Put a dot.
Again: right 1,
up 2.
Dot.
We can also go back: left 1,
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 = 1 and x = 2.
Put x = 1 in.
We get y = 3.
y = 2(1) + 1 = 2 + 1 = 3
3
The point (1, 3) is on our line.
Now x = 2 in.
We get y = 5.
y = 2(2) + 1 = 4 + 1 = 5
5
The point (2, 5) 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.
▶ Watch it solved
The question
Question: graph y = −x − 2.
y = −x − 2
1 Read m and b
b is the number on its own: −2.
The line crosses the y-axis at −2.
That point is called the y-intercept.
b = −2 → start at −2
−x means −1x, so m = −1.
It is the slope.
As a fraction: −1/1.
The bottom is the run: right 1.
The top is the rise: down 1.
m = −1 = −11 → right 1, down 1
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 −2.
Put a dot.
3 Use the slope
From the dot, go right 1,
then down 1.
Put a dot.
Again: right 1,
down 1.
Dot.
We can also go back: left 1,
up 1.
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 = −3.
y = −1 − 2 = −3
−3
The point (1, −3) is on our line.
Now x = 2 in.
We get y = −4.
y = −2 − 2 = −4
−4
The point (2, −4) 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.
▶ Watch it solved
The question
Question: graph y = −(4/3)x + 1.
y = −43x + 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.
b = 1 → start at 1
m is the number in front of x: −4/3.
It is the slope.
The bottom is the run: right 3.
The top is the rise: down 4.
m = −43 → right 3, down 4
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 down 4.
Put a dot.
Again: right 3,
down 4.
Dot.
We can also go back: left 3,
up 4.
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 = −3.
y = −43(3) + 1 = −4 + 1 = −3
−3
The point (3, −3) is on our line.
Now x = 6 in.
We get y = −7.
y = −43(6) + 1 = −8 + 1 = −7
−7
The point (6, −7) 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.
▶ Watch it solved
