Find the variation constant and an equation of variation where Y varies directly as X and Y=60 when X=10

k=variation constant
y=equation of variation

Still do not understand..please..

If y varies directly as x, it means that

y = kx

where k is called the variation constant. That is, y is always some multiple of x. It varies "directly".

So, we want to find k. To do that, we need to know both x and y. Luckily, they have said that y=60 when x=10. Plug them into the equation:

60 = k*10
k=6

So, now we know that y=6x

Aha...thank you..

To find the variation constant and an equation of variation where Y varies directly as X, we start with the given information: Y = 60 when X = 10.

In a direct variation, the equation is of the form Y = kX, where k is the variation constant.

To find the variation constant (k), we substitute the given values into the equation:

60 = k * 10

To solve for k, divide both sides of the equation by 10:

60/10 = k

Simplifying the equation, we have:

6 = k

Therefore, the variation constant (k) is 6.

Now that we have the variation constant, we can write the equation of variation:

Y = kX

Substituting the value of k we found earlier, the equation becomes:

Y = 6X

Hence, the variation constant is 6 and the equation of variation is Y = 6X.

To find the variation constant and equation of variation, we need to understand the concept of direct variation. In direct variation, two quantities are directly proportional to each other, which means that as one quantity increases or decreases, the other quantity also increases or decreases by the same factor.

The equation for direct variation takes the form: Y = kX, where Y is the dependent variable, X is the independent variable, and k is the variation constant.

To find the variation constant, we can use the given values Y = 60 when X = 10. We can substitute these values into the equation Y = kX:

60 = k * 10

Now, we need to solve for k. Divide both sides of the equation by 10:

60/10 = k

Simplifying, we find:

6 = k

So, the variation constant, k, is equal to 6.

Using this value of k, we can write the equation of variation:

Y = 6X

This equation represents the direct variation relationship between Y and X.

I hope this explanation helps you understand the process of finding the variation constant and equation of variation in a direct variation problem.