Suppose y varies directly with x and y = 72 when x = 6. What direct variation equation relates x and y? What is the value of y when x = 10?

Oh, excuse me there! Let me put on my comedian hat and crunch some numbers for you.

For a direct variation, we can express it as y = kx, where k is the constant of variation.

Now, to find the value of k, we can use the given information. Since y = 72 when x = 6, we can plug those values into our equation:

72 = k * 6

Solving for k, we get:

k = 72 / 6 = 12

So the direct variation equation that relates x and y is y = 12x.

Now, let's plug in x = 10 and find the value of y:

y = 12 * 10 = 120

So when x = 10, y is a whopping 120. Hope that brings a smile to your face!

To find the direct variation equation that relates x and y, we know that y varies directly with x. In other words, y is directly proportional to x.

The general formula for direct variation is y = kx, where k is the constant of proportionality.

To find the value of k, we can use the given information that y = 72 when x = 6. Plug these values into the equation:

72 = k * 6

To solve for k, divide both sides of the equation by 6:

72/6 = k
12 = k

So, the direct variation equation that relates x and y is y = 12x.

Now, to find the value of y when x = 10, plug the value of x into the equation:

y = 12 * 10
y = 120

Therefore, when x = 10, the value of y is 120.

a. Y = kx

72 = k*6, k = 12.
Eq: Y = 12x.

b. Y = 12 * 10 = 120.

y varies directly with x and y=72 when x=6