Worked examples
The question
Question: is this table linear: x is 0, 1, 2, 3, and y is 1, 3, 7, 13?
x: 0, 1, 2, 3; y: 1, 3, 7, 13
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 2, then plus 4, then plus 6.
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
▶ Watch it solved
The question
Question: is this table linear: x is 1, 3, 5, 7, and y is 2, 8, 14, 20?
x: 1, 3, 5, 7; y: 2, 8, 14, 20
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 6, then plus 6, then plus 6.
x goes up by 2.
So we divide each change of y by the change of x.
= each 1 of x: 62 = 3, 62 = 3, 62 = 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
▶ Watch it solved
The question
Question: is this table linear: x is 0, 5, 10, 15, and y is 2, 4, 6, 8?
x: 0, 5, 10, 15; y: 2, 4, 6, 8
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 2, then plus 2, then plus 2.
x goes up by 5.
So we divide each change of y by the change of x.
= each 1 of x: 25 = 0.4, 25 = 0.4, 25 = 0.4
The same number every time.
So it is linear.
= always 0.4 → linear
2 Check
Let's check: the changes for each 1 of x are 0.4, 0.4, 0.4.
All the same.
So the answer is right!
0.4, 0.4, 0.4: the same
Let's look back.
First: check the changes.
Last: check.
Answer = always 0.4 → linear
▶ Watch it solved
