Step by step
The question
Question: graph −x + 3y = 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.
3 times 0 is 0.
Adding 0 changes nothing.
−x means −1 times x.
We want just x.
To remove times −1, we divide by −1.
We do it on both sides, so they stay equal.
−1 divided by −1 is 1.
So just x is left.
Plus over minus is minus.
6 divided by −1 is −6.
So x = −6.
So the line crosses the x-axis at (−6, 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.
1 times 0 is 0.
0 plus 3y is just 3y.
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.
3 divided by 3 is 1.
So just y is left.
6 divided by 3 is 2.
So y = 2.
So the line crosses the y-axis at (0, 2).
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: (−6, 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, 1).
It sits on a grid corner.
Put x = −3 and y = 1 into −x + 3y.
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.