Question

name:
grade math ia 1, l088 (proportional relationships)
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.
2. how many cups of fruit would be needed for 9 cups of nuts? show or explain how you know.
3. make a table of the graph above. include at least five pairs of values.

(graph: x - axis labeled nuts (cups), y - axis labeled fruit (cups), with points plotted at (1,2), (2,4), (3,6), (4,8))

Explanation:

Step1: Define proportional relationship

For a proportional relationship $y = kx$, $k = \frac{y}{x}$, where $y$ = fruit (cups), $x$ = nuts (cups).

Step2: Calculate k using a point

Use point $(1,2)$:
$k = \frac{2}{1} = 2$

Step3: Explain the constant's meaning

The constant $k=2$ means for every 1 cup of nuts, 2 cups of fruit are used in the granola bar recipe.

Step4: Solve for nuts with 10 fruit

Rearrange $y=kx$ to $x=\frac{y}{k}$. Substitute $y=10$, $k=2$:
$x = \frac{10}{2} = 5$

Step5: Solve for fruit with 9 nuts

Use $y=kx$. Substitute $x=9$, $k=2$:
$y = 2 \times 9 = 18$

Step6: Create value table

Extract points from the graph and add pairs:

Nuts (cups)	Fruit (cups)
1	2
2	4
3	6
4	8
5	10

Answer:

1. 2
2. For every 1 cup of nuts, the recipe uses 2 cups of fruit.
3. 5 cups of nuts
4. 18 cups of fruit

5.

Nuts (cups)	Fruit (cups)
1	2
2	4
3	6
4	8
5	10