Question

problems 2 - 3: each table represents a proportional relationship. determine the constant of proportionality that completes each equation
2.

s	p
3	12
5	20
10	40

p = _ s
3.

d	c
3	9.42
5	15.7
10	31.4

c = _ d

Explanation:

Step1: Recall the formula for proportionality

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

Step2: Calculate the constant for the first table

For the table with columns $s$ and $P$, using the first - row values $s = 2$ and $P = 8$, we find $k_1=\frac{P}{s}=\frac{8}{2}=4$. We can check with other rows: for $s = 3$ and $P = 12$, $\frac{12}{3}=4$; for $s = 5$ and $P = 20$, $\frac{20}{5}=4$; for $s = 10$ and $P = 40$, $\frac{40}{10}=4$.

Step3: Calculate the constant for the second table

For the table with columns $d$ and $C$, using the first - row values $d = 2$ and $C = 6.28$, we find $k_2=\frac{C}{d}=\frac{6.28}{2}=3.14$. We can check with other rows: for $d = 3$ and $C = 9.42$, $\frac{9.42}{3}=3.14$; for $d = 5$ and $C = 15.7$, $\frac{15.7}{5}=3.14$; for $d = 10$ and $C = 31.4$, $\frac{31.4}{10}=3.14$.

Answer:

$P = 4s$, $C = 3.14d$