Question

study the example showing one way to determine whether a relationship is proportional. then solve problems 1 - 7.
example
the tables show the prices for ordering photo mugs from two different companies. you can use the information to write ratios showing the relationship between the cost and the corresponding number of mugs.
company a
company b
\\( \frac { 15 } { 5 } = 3 \quad \frac { 30 } { 10 } = 3 \quad \frac { 75 } { 25 } = 3 \quad \frac { 150 } { 50 } = 3 \\)
\\( \frac { 20 } { 5 } = 4 \quad \frac { 35 } { 10 } = 3.5 \quad \frac { 80 } { 25 } = 3.2 \quad \frac { 155 } { 50 } = 3.1 \\)
these ratios are all equivalent.
these ratios are not all equivalent.
this relationship is proportional.
this relationship is not proportional.
1 explain how you can tell whether a group of ratios represents a proportional relationship.
2 look at the ratios for company a in the example. what is the constant of proportionality, and what does it mean?
3 write an equation to represent the relationship between the number of mugs and cost for company a. use \\( c \\) for cost and \\( m \\) for the number of mugs.
4 complete the table to show a proportional relationship. write the constant of proportionality.
constant of proportionality:

Explanation:

Step1: Find the constant of proportionality

For the row with \(4\) yoga classes and cost \(\$60\), the constant of proportionality \(k=\frac{y}{x}\) (where \(y\) is cost and \(x\) is the number of classes). So \(k = \frac{60}{4}=15\).

Step2: Calculate the missing values

For \(x = 2\): \(y=k\times x\), so \(y = 15\times2=30\).
For \(x = 6\): \(y=15\times6 = 90\).
For \(x = 8\): \(y=15\times8=120\).

Answer:

Number of Yoga Classes	2	4	6	8

constant of proportionality: \(15\)