Question

write three ordered pairs for direct variation relationship where y= 12 when x= 16

Answer 1

Ordered pairs that work for this direct variation are (4, 3), (8, 6) and (12, 9).

In order to find these, we must first find the value of the direct variation coefficient. We can do that using the base equation y = kx and then by plugging in to find k.

y = kx

12 = k(16)

3/4 = k

Now that we have k, we can model the equation as y = 3/4x. We can also find any number of ordered pairs by using the x value and finding the y value. All of the above answers work.

Answer 2

Given a direct variation where y = 12 when x = 16, three set pf pairs for this variation can be:

(4, 3);  (8, 6); (20, 15)

Recall:

Direct variation can be modelled using the equation: y = kx

k is the constant of proportionality

k = y/x

If y = 12, when x = 16, the constant of proportionality would be:

k = $\frac{12}{16} = \frac{3}{4}$

• The equation would therefore be,

$y = \frac{3}{4} x$

We can use this equation to get three pairs of ordered pairs as follows:

• If x = 4, therefore:

$y = \frac{3}{4} \times 4\\\\y = 3$

• That is: (4, 3)

• If x = 8, therefore:

$y = \frac{3}{4} \times 8\\\\y = 6$

• That is: (8, 6)

• If x = 20, therefore:

$y = \frac{3}{4} \times 20\\\\y = 15$

• That is: (20, 15)

Therefore, given a direct variation where y = 12 when x = 16, three set pf pairs for this variation can be:

(4, 3);  (8, 6); (20, 15)

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