Suppose that y varies directly with x, and y=15 when x=6.
y = k x ... 15 = 6 k ... k = 5/2
To find the direct variation equation that relates y and x, you can use the formula for direct variation which is y = kx, where k is the constant of variation.
Given that y = 15 when x = 6, we can substitute these values into the equation:
15 = k * 6
To find the value of k, we can rearrange the equation to isolate k:
k = 15/6
Simplifying this fraction, we get:
k = 5/2
Therefore, the direct variation equation that relates y and x is:
y = (5/2) * x
To solve this problem, we need to use the concept of direct variation. In direct variation, two variables are directly proportional to each other.
If y varies directly with x, it means that as x increases or decreases, y will also increase or decrease by the same factor. In other words, the ratio between y and x remains constant.
To find the direct variation equation, we can use the formula:
y = kx
Where k is the constant of variation.
We are given that when x=6, y=15. We can substitute these values into the equation:
15 = k * 6
Now we need to solve for k. We can do this by dividing both sides of the equation by 6:
15/6 = k
Simplifying, we get:
k = 2.5
So the equation for the direct variation is:
y = 2.5x
This means that as x increases or decreases, y will change by a factor of 2.5.