Step by step
The question
Question: is 2x + 3y = 6 linear?
2x + 3y = 6
Linear means: a straight line.
y changes by the same amount every time x goes up by 1.
linear = y changes by the same amount
for each 1 of x
1 Look at the x
x and y are only to the power 1, and they are not multiplied together.
= x and y only to the power 1
A table of values shows it.
We put in a few x values and work out y.
2 Check the changes
From one y to the next: minus 2, then minus 2.
x goes up by 3.
So we divide each change of y by the change of x.
= each 1 of x: −23 = −23, −23 = −23
The same number every time.
So it is linear.
= always −2/3 → linear
Careful!
It is not in the y = mx + b form.
But x and y are only to the power 1, so it is still a line.
Careful: not y = ... yet, but still a line
3 Check
Let's check on a graph.
We put in the points.
They are all on one straight line.
So the answer is right!
Let's look back.
First: look at the x.
Then: check the changes.
Last: check.
Answer
Careful: not y = ... yet, but still a line