Step by step
The question
Question: is this table linear: x is 0, 1, 3, 4, and y is 2, 3, 9, 14?
x: 0, 1, 3, 4; y: 2, 3, 9, 14
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 6, then plus 5.
x goes up by different amounts.
So we divide each change of y by the change of x.
= each 1 of x: 11 = 1, 62 = 3, 51 = 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: the changes for each 1 of x are 1, 3, 5.
Not all the same.
So the answer is right!
1, 3, 5: not the same
Let's look back.
First: check the changes.
Last: check.
Answer
Careful: it goes up every time, but by different amounts