Question

katie and her friends set out to sea on their annual fishing trip. there is a proportional relationship between the time (in hours) katie and her friends spend sailing, x, and their distance from shore (in miles), y.

x (hours)	y (miles)
3	12
4	16
5	20

what is the constant of proportionality? write your answer as a whole number or decimal. miles per hour

Explanation:

Step1: Recall the formula for constant of proportionality

For a proportional relationship $y = kx$, the constant of proportionality $k=\frac{y}{x}$.

Step2: Choose a pair of values from the table

Let's take the first - pair $(x = 1,y = 4)$. Then $k=\frac{y}{x}=\frac{4}{1}$.

Step3: Calculate the value of $k$

$\frac{4}{1}=4$. We can check with other pairs. For example, when $x = 3,y = 12$, $k=\frac{y}{x}=\frac{12}{3}=4$; when $x = 4,y = 16$, $k=\frac{y}{x}=\frac{16}{4}=4$; when $x = 5,y = 20$, $k=\frac{y}{x}=\frac{20}{5}=4$.

Answer:

4