Step by step
The question
Question: is y = −2x + 7 linear?
y = −2x + 7
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 is only to the power 1: no squares, nothing at the bottom.
= x 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, then minus 2.
The same number every time.
So it is linear.
= always −2 → linear
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
= always −2 → linear