Question

Determine which variation model represented by the ordered pairs (x, y) is of the form y = kx or y = k/x. (5, −1.5), (10, −3), (15, −4.5), (20, −6), (25, −7.5).

Options:
Option 1: y = kx
Option 2: y = k/x

Answer 1

The variation model represented by the ordered pairs is y = kx.

Step-by-step explanation:

To determine which variation model is represented by the ordered pairs, we need to examine if the relationship between x and y follows the form of either y = kx or y = k/x. Let's check each pair:

For the pair (5, -1.5), if we divide -1.5 by 5, we get -0.3. Therefore, this pair does not follow the form of y = kx.

For the pair (10, -3), if we divide -3 by 10, we get -0.3. Therefore, this pair follows the form of y = kx.

For the pair (15, -4.5), if we divide -4.5 by 15, we get -0.3. Therefore, this pair follows the form of y = kx.

For the pair (20, -6), if we divide -6 by 20, we get -0.3. Therefore, this pair follows the form of y = kx.

For the pair (25, -7.5), if we divide -7.5 by 25, we get -0.3. Therefore, this pair follows the form of y = kx.

Based on our analysis, all the pairs have a constant ratio of -0.3 between y and x, which is the value of k for the equation y = kx. Therefore, the correct variation model represented by the ordered pairs is Option 1: y = kx.