is y varies iversely with x, and why y =-16 when x=-64, what is the constant of variation

Well, if y varies inversely with x, it means that as x increases, y decreases, and vice versa. So, let's take a look at the given values: y = -16 when x = -64.

To find the constant of variation, we can use the formula for inverse variation, which is y = k/x. We can substitute the given values into this equation:

-16 = k/(-64)

Now, let's solve for k. Multiplying both sides by -64, we get:

-16 * (-64) = k

Now it's time to calculate:

1024 = k

So, the constant of variation (k) is 1024.

Now, isn't it funny how things can vary inversely? One goes up, the other goes down. It's like doing the opposite dance moves!

If y varies inversely with x, it means that when x increases, y decreases, and vice versa. Mathematically, this can be represented by the equation y = k/x, where k is the constant of variation.

Now, let's use the given information to find the constant of variation:

We know that y = -16 when x = -64. Substituting these values into the equation, we get:

-16 = k / -64

To solve for k, we can multiply both sides of the equation by -64:

(-16)(-64) = k

Taking the product of -16 and -64, we get:

1024 = k

Therefore, the constant of variation, k, is equal to 1024.

To find the constant of variation when y varies inversely with x, we can use the formula:

y = k/x,

where k is the constant of variation.

Given that y = -16 when x = -64, we can substitute these values into the formula:

-16 = k/-64.

To solve for k, we can cross-multiply:

-16 * -64 = k.

Multiplying the numbers on the left side gives us:

1024 = k.

Therefore, the constant of variation is k = 1024.

xy = k

now just plug in your numbers.