Step by step
The question
Question: graph −3x + 2y = 6.
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.
2 times 0 is 0.
Adding 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.
Plus over minus is minus.
6 divided by −3 is −2.
So x = −2.
So the line crosses the x-axis at (−2, 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 plus 2y is just 2y.
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.
2 divided by 2 is 1.
So just y is left.
6 divided by 2 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: (−2, 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, −3).
It sits on a grid corner.
Put x = −4 and y = −3 into −3x + 2y.
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.