Question

name
7th grade math ia 3, l068 (proportional relationships)
uncommon schools /
date
team
constant of proportionality - graphs
homework
a cereal company is developing a new granola bar. it follows a recipe based on the
graph shown below.

1. what is the constant of proportionality?
2. explain what the constant of proportionality

means for this example. your response should
mention
uts\ and \fruit\.

1. how many cups of nuts would be needed for 10 cups of fruit?

show or explain how you know.

1. how many cups of fruit would be needed for 9 cups of nuts?

show or explain how you know.

1. make a table of the graph above. include at least five pairs of values.

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Explanation:

Question 1:

Step1: Recall the formula for constant of proportionality

For a proportional relationship \( y = kx \), the constant of proportionality \( k=\frac{y}{x} \), where \( x \) is the number of cups of nuts and \( y \) is the number of cups of fruit.

Step2: Use a point from the graph

From the graph, when \( x = 1 \) (nuts), \( y = 2 \) (fruit). So \( k=\frac{y}{x}=\frac{2}{1} = 2 \).

The constant of proportionality \( k = 2 \) means that for every 1 cup of nuts used in the granola bar recipe, 2 cups of fruit are used. So the ratio of fruit to nuts is 2:1, indicating the proportional relationship between the amount of nuts and fruit.

Step1: Use the proportional relationship

We know \( y=kx \), and \( k = 2 \), so \( y = 2x \). We need to find \( x \) when \( y = 10 \) (fruit).

Step2: Solve for \( x \)

Substitute \( y = 10 \) into \( y=2x \), we get \( 10=2x \). Divide both sides by 2: \( x=\frac{10}{2}=5 \).

Answer:

The constant of proportionality is \( 2 \).

Question 2: