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Which table represents a linear function?

Which table represents a linear function?-example-1

2 Answers

3 votes

Answer:

Third Option

Explanation:

We know that a function is linear if its slope or "rate of change" remains constant throughout the domain of the function.

A linear equation has the following formula:


y = mx + b where m is the constant rate of change.

So if
y = f (x)

For any x value, it is always true that:


f(x + 1) - f (x) = m

Notice that among the options given the only table where this is fulfilled is in the third table


f (1 + 1) - f (1) = m\\f (2) -f (1) = m\\-5 - (- 3) = -2 = m\\


f (3) -f (2) = m\\-7 - (- 5) = -2 = m


f (4) - f (3) = m\\-9 - (- 7) = -2 = m

m is constant. Therefore the function is linear

User Leandro Bardelli
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2 votes
ANSWER

Third table

EXPLANATION

The table that represents a linear function has a constant difference in both the x-values and the y-values.

The x-values are having a constant difference of 1 for all the tables.

First table.

Difference in y: 12-6≠6-3

Second Table

Difference in y: 9-5≠5-2

Third table

Difference in y:


- 5 - - 3 = - 7 - - 5 = - 9 - - 7 = - 2

Fourth table.

Different in y:-4--2≠-2--4

Hence the third table is the correct choice.
User Thatguy
by
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