Step by step
The question
Question: graph 3x − 4y = 12.
Every point on the x-axis has y = 0.
Every point on the y-axis has x = 0.
1 Cross the x-axis
On the x-axis, y = 0.
Put 0 in place of y.
4 times 0 is 0.
Taking away 0 changes nothing.
3x means 3 times x.
We want just x.
To remove times 3, we divide by 3.
We do it on both sides, so they stay equal.
3 divided by 3 is 1.
So just x is left.
12 divided by 3 is 4.
So x = 4.
So the line crosses the x-axis at (4, 0).
This point is called the x-intercept.
2 Cross the y-axis
On the y-axis, x = 0.
Put 0 in place of x.
3 times 0 is 0.
0 minus 4y is −4y.
−4y means −4 times y.
We want just y.
To remove times −4, we divide by −4.
We do it on both sides, so they stay equal.
−4 divided by −4 is 1.
So just y is left.
Plus over minus is minus.
12 divided by −4 is −3.
So y = −3.
So the line crosses the y-axis at (0, −3).
This point is called the y-intercept.
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, −3).
Join the dots with a straight line.
It keeps going both ways.
4 Check
Let's check with another point on the line: (−4, −6).
It sits on a grid corner.
Put x = −4 and y = −6 into 3x − 4y.
We get 12, 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.