Question

A baker, in 70 minutes, iced 40 cupcakes and, in 49 minutes, iced 28 cupcakes. What is the constant of proportionality?

Answer 1

`(4)/(7)`

Explanation:

The constant of proportionality is the slope of the line joining the two points

(70,40) and (49,28).

Recall the slope formula:

`m = ( y_2 - y_1 )/( x_2 - x_1)`

We substitute the point to get:

`m = (28 - 40)/(49 - 70) = ( - 12)/( - 21) = (4)/(7)`

Alternatively:

A proportional relation is given by

`y = kx`

where k is the constant of proportionality.

Using any point, we substitute and solve for k.

`40 = 70k`

`k = (40)/(70) = (4)/(7)`