The value of y varies directly with x. If x=10, then y=6

What is the value of x when y=9?

To find the value of x when y=9, we can set up a proportion using the direct variation relationship.

Since the value of y varies directly with x, we can write the proportion as:

y/x = k

where k is the constant of variation.

Using the given information, we can substitute the values:

6/10 = k

To find k, divide 6 by 10:

k = 6/10 = 0.6

Now we can use the proportion to find x when y=9:

9/x = k

Substitute the value of k:

9/x = 0.6

To find x, cross-multiply:

9 = 0.6x

Divide both sides by 0.6:

9/0.6 = x

Simplifying the right side:

15 = x

Therefore, when y=9, x=15.

To find the value of x when y=9, we can use the concept of direct variation.

Direct variation can be represented using the equation y = kx, where k is the constant of variation.

Given that when x=10, y=6, we can substitute these values into our equation:

6 = k(10)

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

6/10 = k

Simplifying, we get:

3/5 = k

Now that we have the value of k, we can substitute it back into the equation and solve for x when y=9:

9 = (3/5)x

To isolate x, we can multiply both sides of the equation by 5/3:

9 * (5/3) = x

Simplifying, we get:

15 = x

Therefore, when y=9, the value of x is 15.

To find the value of x when y = 9, we can use the given information that y varies directly with x. This means that there is a constant of variation (k) that relates the two variables.

In this case, if x = 10, then y = 6. We can use this information to find the constant of variation (k).

To find k, we can use the formula for direct variation:
y = kx

Plugging in the given values, we have:
6 = 10k

Solving for k, we divide both sides by 10:
k = 6/10
k = 0.6

Now that we know the constant of variation, we can find the value of x when y = 9 by rearranging the equation:
y = kx

Plugging in the values, we have:
9 = 0.6x

We can solve for x by dividing both sides by 0.6:
x = 9/0.6
x = 15

Therefore, when y = 9, the value of x is 15.