Step by step
The question
Question: is this table linear: x is 0, 2, 4, 6, and y is 1, 2, 5, 10?
x: 0, 2, 4, 6; y: 1, 2, 5, 10
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
We write it as a table.
1 Check the changes
From one y to the next: plus 1, then plus 3, then plus 5.
x goes up by 2.
So we divide each change of y by the change of x.
= each 1 of x: 12 = 0.5, 32 = 1.5, 52 = 2.5
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
2 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: check the changes.
Last: check.
Answer
Careful: it goes up every time, but by different amounts