Question

1. a bakery sells round loaves of bread and pans of rolls. the graph shows the relationship between the number of each type of bread and the number of servings. select all the statements that are true, based on the graph.

□ a. both lines show a proportional relationship between the number of each type of bread and the number of servings.
□ b. 2 pans of rolls can serve 28 people.
□ c. there are 4 servings in 16 round loaves.
□ d. there are more servings in a round loaf than in a pan of rolls.
□ e. a round loaf serves less people than a pan of rolls.
□ f. the line that represents the number of servings in a pan of rolls has a greater constant of proportionality.

Explanation:

Step1: Check proportionality

Proportional relationships pass through the origin \((0,0)\). Both lines pass through \((0,0)\), so statement A is true.

Step2: Analyze statement B

For pans of rolls, when \(x = 2\) (number of pans), \(y=28\) (servings). So 2 pans of rolls serve 28 people. Statement B is true.

Step3: Analyze statement C

For round loaves, if \(x = 16\), \(y
eq4\). The relationship for round loaves: \(y = 4x\) (from graph, when \(x = 1,y = 4\)). When \(x=16,y=64\). Statement C is false.

Step4: Analyze statement D

For a round loaf (\(x = 1\)), \(y = 4\) (servings). For a pan of rolls (\(x = 1\)), \(y=14\). So there are fewer servings in a round loaf than in a pan of rolls. Statement D is false.

Step5: Analyze statement E

As in step 4, when \(x = 1\), round loaf \(y = 4\), pan of rolls \(y=14\). A round loaf serves less people than a pan of rolls. Statement E is true.

Step6: Analyze statement F

Constant of proportionality \(k=\frac{y}{x}\). For round loaves \(k_{1}=\frac{y}{x}=4\) (e.g., \(x = 1,y = 4\)). For pans of rolls \(k_{2}=\frac{y}{x}=14\) (e.g., \(x = 1,y = 14\)). The line for pans of rolls has a greater constant of proportionality. Statement F is true.

Answer:

A. Both lines show a proportional relationship between the number of each type of bread and the number of servings.
B. 2 pans of rolls can serve 28 people.
E. A round loaf serves less people than a pan of rolls.
F. The line that represents the number of servings in a pan of rolls has a greater constant of proportionality.