Question

Determine whether y varies with x. If so, find the constant of variation and write the function rule.

x | y
56 | 14
80 | 20
88 | 22

Does y vary directly with x?
O No
O Yes

Answer 1

Answer: Yes, y does vary directly with x.

Constant of variation = 1/4

The function rule is y = (1/4)x

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Step-by-step explanation:

Let's assume that y does vary directly with x.

If that's the case, then we have an equation in the form y = kx, where k is the constant of variation.

Solving for k gets us k = y/x

For each row, divide the y value over the x value

• row one: k = y/x = 14/56 = 0.25
• row two: k = y/x = 20/80 = 0.25
• row three: k = y/x = 22/88 = 0.25

Each row yields the value k = 0.25 and it fully confirms y does vary directly with x.

So y = kx becomes y = 0.25x as the function rule, which is equivalent to y = (1/4)x