Question

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

X
7
8
y
14
16
9 15
10 17
Determine whether y varies directly with x. If so, find the constant of variation k and write the equation. (2 points

Answer 1

The variable y varies directly with x, as evidenced by a consistent ratio of y to x for the given pairs of values, which is 2. The constant of variation k is 2, and the direct variation equation is y = 2x.

Step-by-step explanation:

Determining if y Varies Directly with x and Finding the Constant of Variation

To determine whether y varies directly with x, we need to check if the ratio of y to x is constant for each pair of values. If y is directly proportional to x, then there exists a constant k such that y = kx. Let's use the given values to find out if y varies directly with x and, if so, to find the value of k.

1. Calculate the ratio of y to x for each pair of numbers: 14/7 = 2, 16/8 = 2.
2. Notice that the ratios are consistent and equal, indicating that y varies directly with x and the constant of variation k is 2.
3. The equation that defines this direct variation is y = 2x.

We confirmed that y varies directly with x by showing the ratios of y to x were equal, and we calculated the constant of variation to be 2, hence providing the direct variation equation.