Question

A graph contains the following points: (4,10)
, (6,12)
, and (8,14)
. What type of rule is represented?(1 point)
Responses

multiplicative, 2x
multiplicative, 2 x

multiplicative, 2y
multiplicative, 2 y

additive, x+6
additive, x plus 6

additive, x+2
additive, x plus 2

Answer 1

To determine the type of rule represented by the points (4,10), (6,12), and (8,14), we can analyze the relationship between the x and y values.

1. For the first point (4, 10): \( y = 2 \times 4 + 2 = 10 \)
2. For the second point (6, 12): \( y = 2 \times 6 + 0 = 12 \)
3. For the third point (8, 14): \( y = 2 \times 8 - 2 = 14 \)

It appears that as x increases by 2, y increases by 2, suggesting a linear (additive) relationship where we can use the form \( y = mx + b \).

Looking for an additive relationship:

y appears to be calculated as:
- For \( x = 4: 10 = x + 6 \)
- For \( x = 6: 12 = x + 6 \)
- For \( x = 8: 14 = x + 6 \)

The rule is \( y = x + 6 \).

Thus, the correct response is:

**additive, x + 6**.