The height of a stack of DVD cases is in a proportional relationship to the number of cases in the stack. A stack of 8 cases and its height are shown. Find the constant of proportionality. Then use the constant of proportionality to find the height of a stack of 13 cases.

a. The equation is y = 19 x

b. The height of 13 DVD cases is 247 mm

Step-by-step explanation:

- A proportional relationship is about two quantities vary directly with

each other

- Ex: If y proportion to x, then y is varies directly with x

 That means y ∝ x ⇒ y = k x, where k is the constant of variation

- The height of a stack of DVD case is proportional to the number of

 case in the stack

- That means the height of DVD cases varies with the number of cases

- The height of 6 DVD case is 114 mm

a.

∵ The number of cases = x

∵ The height of the cases = y

∴ y ∝ x

∴ y = k x

- To find k lets use the first information above

∵ y = 114 mm when x = 6

- Substitute these values in the equation above to find k

∵ 114 = 6 k

- Divide both sides by 6

∴ k = 19

- Substitute the value of k in the equation above

∴ y = 19 x

* The equation is y = 19 x

b.

- We need to find the height of 13 DVD cases

∵ y = 19 x

∵ x = 13

- Substitute the value of x in the equation

∴ y = 19 × 13

∴ y = 247 mm

* The height of 13 DVD cases is 247 mm