Step by step
The question
Question: is this table linear: x is 1, 2, 4, 5, and y is 5, 8, 14, 17?
x: 1, 2, 4, 5; y: 5, 8, 14, 17
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 3, then plus 6, then plus 3.
x goes up by different amounts.
So we divide each change of y by the change of x.
= each 1 of x: 31 = 3, 62 = 3, 31 = 3
The same number every time.
So it is linear.
= always 3 → linear
2 Check
Let's check: the changes for each 1 of x are 3, 3, 3.
All the same.
So the answer is right!
3, 3, 3: the same
Let's look back.
First: check the changes.
Last: check.
Answer
= always 3 → linear