Step by step
The question
Question: is y = 12/x + 1 linear?
y = 12x + 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
x is at the bottom of a fraction.
That bends the line.
= x is at the bottom of a fraction
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 6, then minus 3.
x goes up by different amounts.
So we divide each change of y by the change of x.
= each 1 of x: −61 = −6, −32 = −1.5
The changes are not the same.
So it is not linear.
= not the same → not linear
Careful!
Going down every time is not enough.
A line changes by the same amount every time.
Careful: it goes down 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 down every time, but by different amounts