Step by step
The question
Question: is y = x² + 1 linear?
y = x² + 1
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
There is x squared: x times x.
That bends the line.
= x² = x × x: x times itself
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: plus 1, then plus 3, then plus 5.
The changes are not the same.
So it is not linear.
= not the same → not linear
Careful!
Going up every time is not enough.
A line changes by the same amount every time.
Careful: it goes up every time, but by different amounts
3 Check
Let's check on a graph.
We put in the points.
The line through the first two points misses the others: the points bend away.
So the answer is right!
Let's look back.
First: look at the x.
Then: check the changes.
Last: check.
Answer
Careful: it goes up every time, but by different amounts