IXL | Write a linear function from a table

Which equation gives the rule for this table?

x	y
0	0
1	^–27
2	^–54
3	^–81

y = ^–27x − 8

y = ^–27x

y = ^–27x − 7

y = ^–27x + 1

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Learn with an example

question

Which equation gives the rule for this table?

x	y
2	42
3	43
4	44
5	45

y = x − 17

y = x − 40

y = x + 17

y = x + 40

key idea

Linear functions are of the form y = mx + b.

solution

First find m. Look at the table and notice that every time the x terms go up by 1, the y terms go up by 1. This means that m is equal to 1.

x	y
2	42
3	43
4	44
5	45

Next find b. Take the equation y = mx + b and plug in the m value (m = 1) and a pair of (x, y) coordinates from the table, such as (2, 42). Then solve for b.

mx + b

Plug in m = 1, x = 2, and y = 42

1(2) + b

Plug in m = 1, x = 2, and y = 42

Simplify

2 + b

Simplify

Finally, use the m and b values you found (m = 1 and b = 40) to write the equation.

mx + b

Plug in m = 1 and b = 40

1x + 40

Plug in m = 1 and b = 40

Simplify

x + 40

Simplify

Now check your answer. Plug in each (x, y) pair in the table, and see if the result is a true statement.

Plug in (2, 42).

x + 40

2 + 40

Plug in (3, 43).

x + 40

3 + 40

Plug in (4, 44).

x + 40

4 + 40

Plug in (5, 45).

x + 40

5 + 40

Each (x, y) pair from the table resulted in a true statement.

So, the equation is y = x + 40.

Looking for more? Try these:

Lesson: Linear functions

Lesson: Slope

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Work it out

Not feeling ready yet? These can help:

Lesson: Linear functions

Lesson: Slope

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