Question

the table shows the price of different amounts of gourmet coffee at a grocery store.
amount of coffee (lb) 1 2 3 4
price (dollars) 8 16 24 32
what is the constant of proportionality in dollars per pound?
the constant of proportionality is .

Explanation:

Step1: Recall the formula for constant of proportionality

The constant of proportionality \( k \) in a proportional relationship \( y = kx \) (where \( y \) is the price and \( x \) is the amount of coffee) is given by \( k=\frac{y}{x} \).

Step2: Calculate using the first pair of values

For \( x = 1 \) (lb) and \( y = 8 \) (dollars), we substitute into the formula: \( k=\frac{8}{1}=8 \). We can verify with other pairs: for \( x = 2 \), \( y = 16 \), \( k=\frac{16}{2}=8 \); for \( x = 3 \), \( y = 24 \), \( k=\frac{24}{3}=8 \); for \( x = 4 \), \( y = 32 \), \( k=\frac{32}{4}=8 \). All give the same value.

Answer:

8