Worked examples
The question
Question: graph 2x + 3y = 6.
2x + 3y = 6
Every point on the x-axis has y = 0.
Every point on the y-axis has x = 0.
on the x-axis: y = 0
on the y-axis: x = 0
1 Cross the x-axis
On the x-axis, y = 0.
Put 0 in place of y.
2x + 3 × 0 = 6
3 times 0 is 0.
Adding 0 changes nothing.
2x = 6
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.
2x2 = 62
2 divided by 2 is 1.
So just x is left.
6 divided by 2 is 3.
62 = 3
So x = 3.
x = 3
So the line crosses the x-axis at (3, 0).
This point is called the x-intercept.
→ (3, 0)
2 Cross the y-axis
On the y-axis, x = 0.
Put 0 in place of x.
2 × 0 + 3y = 6
2 times 0 is 0.
0 plus 3y is just 3y.
3y = 6
3y means 3 times y.
We want just y.
To remove times 3, we divide by 3.
We do it on both sides, so they stay equal.
3y3 = 63
3 divided by 3 is 1.
So just y is left.
6 divided by 3 is 2.
63 = 2
So y = 2.
y = 2
So the line crosses the y-axis at (0, 2).
This point is called the y-intercept.
→ (0, 2)
3 Draw the line
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.
Put the two points on the grid: (3, 0)
and (0, 2).
Join the dots with a straight line.
It keeps going both ways.
4 Check
Let's check with another point on the line: (−3, 4).
It sits on a grid corner.
Put x = −3 and y = 4 into 2x + 3y.
2(−3) + 3(4) = −6 + 12 = 6
We get 6, the same as the right side.
So the line is right!
Let's look back.
First: cross the x-axis.
Then: cross the y-axis.
Then: draw the line.
Last: check.
▶ Watch it solved
The question
Question: graph x − 2y = 4.
x − 2y = 4
Every point on the x-axis has y = 0.
Every point on the y-axis has x = 0.
on the x-axis: y = 0
on the y-axis: x = 0
1 Cross the x-axis
On the x-axis, y = 0.
Put 0 in place of y.
x − 2 × 0 = 4
2 times 0 is 0.
Taking away 0 changes nothing.
So x = 4.
x = 4
So the line crosses the x-axis at (4, 0).
This point is called the x-intercept.
→ (4, 0)
2 Cross the y-axis
On the y-axis, x = 0.
Put 0 in place of x.
0 − 2y = 4
0 minus 2y is −2y.
−2y = 4
−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.
−2y−2 = 4−2
−2 divided by −2 is 1.
So just y is left.
Plus over minus is minus.
4 divided by −2 is −2.
4−2 = −2
So y = −2.
y = −2
So the line crosses the y-axis at (0, −2).
This point is called the y-intercept.
→ (0, −2)
3 Draw the line
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.
Put the two points on the grid: (4, 0)
and (0, −2).
Join the dots with a straight line.
It keeps going both ways.
4 Check
Let's check with another point on the line: (2, −1).
It sits on a grid corner.
Put x = 2 and y = −1 into x − 2y.
2 − 2(−1) = 2 + 2 = 4
We get 4, the same as the right side.
So the line is right!
Let's look back.
First: cross the x-axis.
Then: cross the y-axis.
Then: draw the line.
Last: check.
▶ Watch it solved
The question
Question: graph 2x + 3y = 0.
2x + 3y = 0
Every point on the x-axis has y = 0.
Every point on the y-axis has x = 0.
on the x-axis: y = 0
on the y-axis: x = 0
1 Cross the x-axis
On the x-axis, y = 0.
Put 0 in place of y.
2x + 3 × 0 = 0
3 times 0 is 0.
Adding 0 changes nothing.
2x = 0
2 times what is 0?
Only 0.
So x = 0.
x = 0
So the line crosses the x-axis at (0, 0).
This point is called the x-intercept.
→ (0, 0)
2 Cross the y-axis
On the y-axis, x = 0.
Put 0 in place of x.
2 × 0 + 3y = 0
2 times 0 is 0.
0 plus 3y is just 3y.
3y = 0
3 times what is 0?
Only 0.
So y = 0.
y = 0
So the line crosses the y-axis at (0, 0).
This point is called the y-intercept.
→ (0, 0)
3 Find one more point
Both crossings are (0, 0): the same point.
One point is not enough for a line.
We need one more point.
We pick x = 3.
3 is the number in front of y, so y comes out whole.
2 × 3 + 3y = 0
2 times 3 is 6.
Now we have 6 + 3y.
6 + 3y = 0
We want 3y by itself.
The 6 is in the way.
To remove 6, we take away 6.
We do it on both sides, so they stay equal.
6 + 3y − 6 = 0 − 6
+ 6 and − 6 make zero.
Cross them out.
0 minus 6 is −6.
3y = −6
3y means 3 times y.
We want just y.
To remove times 3, we divide by 3.
We do it on both sides, so they stay equal.
3y3 = −63
3 divided by 3 is 1.
So just y is left.
Minus over plus is minus.
−6 divided by 3 is −2.
−63 = −2
So y = −2.
y = −2
So (3, −2) is on the line too.
→ (3, −2)
4 Draw the line
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.
Put the two points on the grid: (0, 0)
and (3, −2).
Join the dots with a straight line.
It keeps going both ways.
5 Check
Let's check with another point on the line: (−3, 2).
It sits on a grid corner.
Put x = −3 and y = 2 into 2x + 3y.
2(−3) + 3(2) = −6 + 6 = 0
We get 0, the same as the right side.
So the line is right!
Let's look back.
First: cross the x-axis.
Then: cross the y-axis.
Then: find one more point.
Then: draw the line.
Last: check.
▶ Watch it solved
