Step by step
The question
Question: graph x − 2y = 0.
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.
Taking away 0 changes nothing.
So x = 0.
So the line crosses the x-axis at (0, 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.
0 minus 2y is −2y.
−2 times what is 0?
Only 0.
So y = 0.
So the line crosses the y-axis at (0, 0).
This point is called the y-intercept.
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 = 2.
2 is the number in front of y, so y comes out whole.
Now we have 2 − 2y.
We want 2y by itself.
The 2 is in the way.
To remove 2, we take away 2.
We do it on both sides, so they stay equal.
+ 2 and − 2 make zero.
Cross them out.
0 minus 2 is −2.
−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.
Minus over minus is plus.
−2 divided by −2 is 1.
So y = 1.
So (2, 1) is on the line too.
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 (2, 1).
Join the dots with a straight line.
It keeps going both ways.
5 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.
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.