Question

look at the ratios for company a in the example. what is the constant of proportionality and what does it mean? 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. complete the table to show a proportional relationship. write the constant of proportionality. constant of proportionality: vocabulary constant of proportionality rate in a proportional relationship

Explanation:

Step1: Define constant of proportionality

For a proportional relationship $y = kx$, $k$ is the constant of proportionality. In the case of cost $c$ and number of mugs $m$, if $c$ is proportional to $m$, the equation is $c=km$. Given when $m = 4$, $c = 60$. We find $k$ by substituting these values into the equation.

Step2: Calculate the constant of proportionality

Substitute $c = 60$ and $m = 4$ into $c=km$. We get $k=\frac{c}{m}=\frac{60}{4}=15$.

Step3: Complete the table

If $m = 2$, then $c=km = 15\times2=30$. If $m = 6$, then $c=15\times6 = 90$. If $m = 8$, then $c=15\times8=120$.

Step4: Write the equation

The equation representing the relationship between the number of mugs and cost for Company A is $c = 15m$.

Step5: Interpret the constant of proportionality

The constant of proportionality 15 means that each mug costs $15$.

Answer:

Constant of proportionality: 15
Completed table:

Number of Mugs ($m$)	Cost ($c$)
4	60
6	90
8	120

Equation: $c = 15m$
Interpretation: Each mug costs $15$.