Question

Relationship A has a greater rate than Relationship B. This table represents Relationship B.

Hours worked 2 4 5 8
Amount paid 30.40 60.80 76 121.60
Which equation could represent Relationship A?

Hours worked is represented by x, and amount paid is represented by y.

Select each correct answer.

Responses

y = 16.4x
y = 16.4 x

y = 15.4x
y = 15.4 x

y = 15.2x
y = 15.2 x

y = 14.9x
y = 14.9 x

Answer 1

To determine which equation could represent Relationship A, we first need to find the rate (or unit rate) of Relationship B based on the given data.

From Relationship B, we can fill in the rate by calculating the amount paid per hour worked using the data in the table.

1. For 2 hours worked (amount paid = 30.40):
- Rate = 30.40 / 2 = 15.20

2. For 4 hours worked (amount paid = 60.80):
- Rate = 60.80 / 4 = 15.20

3. For 5 hours worked (amount paid = 76):
- Rate = 76 / 5 = 15.20

4. For 8 hours worked (amount paid = 121.60):
- Rate = 121.60 / 8 = 15.20

The unit rate for Relationship B is consistently 15.20.

Since Relationship A has a greater rate than Relationship B, we are looking for equations with rates greater than 15.20.

Looking at the responses:

- y = 16.4x: Greater than 15.20 (Valid)
- y = 15.4x: Greater than 15.20 (Valid)
- y = 15.2x: Equal to Relationship B (Not Valid)
- y = 14.9x: Less than 15.20 (Not Valid)

Thus, the correct answers that represent Relationship A are:

- y = 16.4x
- y = 15.4x