Step by step
The question
Question: graph 2x + 3y = 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.
3 times 0 is 0.
Adding 0 changes nothing.
2 times what is 0?
Only 0.
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.
2 times 0 is 0.
0 plus 3y is just 3y.
3 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 = 3.
3 is the number in front of y, so y comes out whole.
2 times 3 is 6.
Now we have 6 + 3y.
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 and − 6 make zero.
Cross them out.
0 minus 6 is −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.
3 divided by 3 is 1.
So just y is left.
Minus over plus is minus.
−6 divided by 3 is −2.
So y = −2.
So (3, −2) 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 (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.
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.