Question

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

Answer 1

Answer:

$\frac{4}{7}$

Step-by-step explanation:

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

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

Recall the slope formula:

$m = \frac{ y_2 - y_1 }{ x_2 - x_1}$

We substitute the point to get:

$m = \frac{28 - 40}{49 - 70} = \frac{ - 12}{ - 21} = \frac{4}{7}$

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.

$40 = 70k$

$k = \frac{40}{70} = \frac{4}{7}$