Question

For the data in the table, does y vary directly with x? If it does, write an equation for the

direct variation.
x y
8 11
16 22
24 33

Answer 1

Below in bold.

Explanation:

The definition of direct variation is y = kx where k is a constant.

So, if y/x is a constant for the data, we have direct variation.

So, checking the rows in the given table:

y/x = 11/8

y/x = 22/16 = 11/8

y/x = 33/24 = 11/8

- we see that this is direct variation.

So, k = 11/8 and

The equation is

y = (11/8) x

or

y = 11x/8

or

y = 1.375x in decimal form.

Answer 2

• y = (11/8)x

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Direct variation equation:

• y = kx, where k- variation coefficient

Use the pairs of coordinates and find the value of k, then compare:

• 11 = 8k ⇒ k = 11/8
• 22 = 16k ⇒ k = 22/16 = 11/8
• 33 = 24k ⇒ k = 33/24 = 11/8

The value of k is same with all ordered pairs and the equation is:

• y = (11/8)x