Question

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write the constant of proportionality.
1 ( y = -2x )
constant of proportionality:

2

minutes	feet
1	5
2	10
3	15
4	20

constant of proportionality:

3 peaches cost $2.50 per pound.
constant of proportionality:

4 the club donates $5 for every 3 doughnuts sold.
constant of proportionality:

Explanation:

Problem 1:

Step1: Recall the form of a proportional equation

A proportional relationship is in the form \( y = kx \), where \( k \) is the constant of proportionality.

Step2: Identify \( k \) in \( y = -2x \)

In the equation \( y=-2x \), comparing with \( y = kx \), we see that \( k=-2 \).

Step1: Recall the formula for constant of proportionality

For a proportional relationship between two quantities \( x \) (Minutes) and \( y \) (Feet), the constant of proportionality \( k=\frac{y}{x} \).

Step2: Calculate \( k \) using a pair of values

Using the values \( x = 1 \) (Minutes) and \( y = 5 \) (Feet), we substitute into the formula: \( k=\frac{5}{1}=5 \). We can check with other pairs (e.g., \( x = 2 \), \( y = 10 \), \( \frac{10}{2}=5 \)) to confirm.

Step1: Define the proportional relationship

Let \( C \) be the cost and \( p \) be the pounds of peaches. The cost of peaches is proportional to the number of pounds, so \( C=kp \), where \( k \) is the constant of proportionality (cost per pound).

Step2: Identify \( k \) from the given cost

We know that peaches cost \( \$2.50 \) per pound, so \( k = 2.50 \).

Answer:

\( -2 \)

Problem 2: