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