Question

for each proportional relationship, write a compare answers with partner a. if you find & fix the error. ① at the grocery store, 2.5 pounds of meat costs $17.50 and 3 pounds of meat costs $21.00. write an equation to represent the price (y) per pound (x) of meat. y=5.8x

Explanation:

Step1: Calculate the unit price

To find the unit price (constant of proportionality \( k \)), we use the formula \( k=\frac{y}{x} \). For the first case, \( x = 2.5 \) pounds and \( y=\$17.50 \). So, \( k=\frac{17.50}{2.5}=7 \). We can verify with the second case: \( x = 3 \) pounds, \( y = \$21.00 \), and \( \frac{21.00}{3}=7 \). So the constant of proportionality \( k = 7 \).

Step2: Write the proportional equation

The general form of a proportional relationship is \( y=kx \). Since \( k = 7 \), the equation should be \( y = 7x \), not \( y = 5.8x \). The error was in calculating the unit price (either miscalculating \( \frac{17.50}{2.5} \) or using an incorrect value for \( k \)).

Answer:

The correct equation is \( y = 7x \). The error in \( y = 5.8x \) was a miscalculation of the unit price (constant of proportionality); the correct unit price is \( 7 \) (since \( \frac{17.50}{2.5}=7 \) and \( \frac{21.00}{3}=7 \)), so the equation should be \( y = 7x \).