Variation Functions

Question

If y varies directly as x, and y = 13 when x = 2, then find x when y = 3. Just type the number. If the answer is not an integer, then write it as a fraction in simplest form, with a slash (/) between the numerator and the denominator.

If y varies inversely as x, and y = 7 when x = 8, then find y when x = 4. Just type the number. If the answer is not an integer, then write it as a fraction in simplest form, with a slash (/) between the numerator and the denominator.

If y varies directly as x, and y = 24 when x = 15, then find y when x = 3. Just type the number. If the answer is not an integer, then write it as a fraction in simplest form, with a slash (/) between the numerator and the denominator.

Answer 1

Direct variation follows the form y = kx

find the constant k by using the given situation

13 = k2. ---->. k = 13/2. = 6.5

So the formula is y = 6.5 x

Then the second situation is 3 = 6.5 x. or 3 = 13/2 x.

so y = 3/6.5 or y = 3/(13/2) = 6/13

Inverse variation is y = k/x

Again, use the first situation to find k

7 = k/8 ------>. k = 56

then y = 56/x so. if x = 4, then y = 56/4 = 14