Question

Which table represents a linear function?

Answer 1

Table 4 represents a linear function as the ratio of the change in y to the change in x is constant (
`2`). The relationship is linear with a slope of
`2`.

A table represents a linear function if the ratio of the change in y to the change in x is constant. Let's check each table:

1. Table 1:

`\( (\Delta y)/(\Delta x) = (2-1)/(1-0) = 1 \)\\ \\ \( (\Delta y)/(\Delta x) = (4-2)/(2-1) = 2 \)\\ \\ \( (\Delta y)/(\Delta x) = (8-4)/(3-2) = 4 \)`

Since the ratio is not constant, Table 1 does not represent a linear function.

2. Table 2:

`\( (\Delta y)/(\Delta x) = (1-0)/(1-0) = 1 \)\\ \\ \( (\Delta y)/(\Delta x) = (3-1)/(2-1) = 2 \)\\ \\ \( (\Delta y)/(\Delta x) = (6-3)/(3-2) = 3 \)`

The ratio is not constant, so Table 2 does not represent a linear function.

3. Table 3:

`\( (\Delta y)/(\Delta x) = (1-0)/(1-0) = 1 \)\\ \\ \( (\Delta y)/(\Delta x) = (0-1)/(2-1) = -1 \) \\ \\ \( (\Delta y)/(\Delta x) = (1-0)/(3-2) = 1 \)`

The ratio is not constant, so Table 3 does not represent a linear function.

4. Table 4:

`\( (\Delta y)/(\Delta x) = (3-1)/(1-0) = 2 \)\\\\ \( (\Delta y)/(\Delta x) = (5-3)/(2-1) = 2 \)\\ \\ \( (\Delta y)/(\Delta x) = (7-5)/(3-2) = 2 \)`

The ratio is constant at
`2`, so Table 4 represents a linear function.

Answer 2

I pretty sure it’s the first one