Question

Identify the constant of the ordered pair and then write the direct variation equation. (10,-2) and (90, -18)

Answer 1

The constant of variation for the ordered pairs (10, -2) and (90, -18) is -0.2. The direct variation equation is y = -0.2x.

Step-by-step explanation:

To identify the constant of variation (k) for the direct variation equation, and then write the equation, follow these steps:

1. Understand that a direct variation between two variables x and y can be represented by the equation y = kx, where k is the constant of variation.
2. Use the given ordered pairs (10, -2) and (90, -18) to find the constant of variation by dividing the y-value of the pair by its corresponding x-value.
3. For the first pair (10, -2), divide -2 by 10 to get k = -0.2.
4. Confirm that k is consistent with the second pair by dividing -18 by 90, which also gives k = -0.2.
5. Now that we've established the constant of variation is -0.2, we can write the direct variation equation as y = -0.2x.