Question

1. each table represents a proportional relationship. for each, find the constant of proportionality, and write an equation that represents the relationship.

s	p
3	12
5	20
10	40
d	c
2	6.28
3	9.42
5	15.7
10	31.4

constant of proportionality:
constant of proportionality:

Explanation:

Step1: Recall proportional - relationship formula

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

Step2: Calculate constant for first table (s and P)

For the first table with variables $s$ and $P$, when $s = 2$ and $P = 8$, $k_1=\frac{P}{s}=\frac{8}{2}=4$. Checking other rows: $\frac{12}{3}=4$, $\frac{20}{5}=4$, $\frac{40}{10}=4$. The equation is $P = 4s$.

Step3: Calculate constant for second table (d and C)

For the second table with variables $d$ and $C$, when $d = 2$ and $C = 6.28$, $k_2=\frac{C}{d}=\frac{6.28}{2}=3.14$. Checking other rows: $\frac{9.42}{3}=3.14$, $\frac{15.7}{5}=3.14$, $\frac{31.4}{10}=3.14$. The equation is $C = 3.14d$.

Answer:

For the first table (s and P): Constant of proportionality is 4, equation is $P = 4s$.
For the second table (d and C): Constant of proportionality is 3.14, equation is $C = 3.14d$.