Question

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

Answer 1

Answer:  Yes, y does vary directly with x.

Constant of variation = 1/4

The function rule is  y = (1/4)x

=========================================================

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