Question

The pair of values below is from a direct variation. Find the missing number.

(4,6) and (x,3)

Answer 1

The answer is 2.

2 since 6/4=3/2

Explanation:

Since your relation is a direct variation then the points on your line are of the form y=kx where k is the constant of variation (also called constant of proportionality)

If y=kx then y/x=k.

So all the points in this relation since it is a direct variation will be equal to y-coordinate/x-coordinate.

So we are going to solve this proportion:

`(6)/(4)=\farc{3}{x}`

Again I put y/x from each point. They should have same ratio because this is a direct variation.

Cross multiply:

`6(x)=4(3)`

`6x=12`

Divide boht sides by 6:

`x=(12)/(6)`

`x=2`

Answer 2

Explanation:

You are solving for the direct variation. This means that the amount of change for is consistent for both x & y:

Note: (x , y) & (x₁ , y₁)

(x , y) = (4 , 6)

(x₁ , y₁) = (x , 3)

Set the two equal to each other:

(4 , 6) = (x , 3)

Find common denominators (y). Remember that what you multiply to one you multiply to the other:

(4 , 6) = (x * 2, 3 * 2) = (2x , 6)

Simplify. Isolate the variable x. Divide:

(4) = (2x)

(4)/2 = (2x)/2

x = 4/2

x = 2

x = 2 is your answer.