A direct variation includes the points (6,18) and (3,n) find n. Write and solve a direct variation equation to find the answer.

Answer 1

In a direct variation equation, the ratio of the two variables remains the same. Let's find the ratio using the given points.

The ratio is equal to the change in y divided by the change in x, so:

ratio = (n - 18) / (3 - 6)

Simplifying the ratio, we have:

ratio = (n - 18) / (-3)

Since the ratio remains the same, it is equal to the ratio of the first given point:

18 / 6 = ratio

Dividing both sides of the equation by 6:

3 = ratio

Substituting this value into the simplified ratio equation:

3 = (n - 18) / (-3)

Multiplying both sides of the equation by -3:

-9 = n - 18

Adding 18 to both sides of the equation:

n = 9

Therefore, n = 9.