Question

6. The variable x and y vary directly, and y = 40 when x = 5. Which equation relates the variables?

A.) y = 1/8 x
B.) y = 4x
C.) y= 40x
D.) y = 8x
E.) none of these

Answer 1

The equation relates the variables is y = 8x ⇒ D

Explanation:

If x and y vary directly (y ∝ x), then y = k x, where

• k is the constant of variation

• k can be found using the initial value of x and y

∵ The variable x and y vary directly

∴ y ∝ x

→ By using the rule above

∴ y = k x

∵ y = 40 when x = 5

∴ The initial values of x and y are x = 5 and y = 40

→ Substitute them in the equation above to find k

∵ 40 = k(5)

∴ 40 = 5k

→ Divide both sides by 5

∵
`(40)/(5)` =
`(5k)/(5)`

∴ 8 = k

→ Substitute the value of k in the equation above

∴ y = 8x

∴ The equation relates the variables is y = 8x