Question

a. which graph is which? give them the correct titles.
b. which quantities appear to be in a proportional relationship? explain how you know.
c. for the proportional relationship, find the constant of proportionality. what does that number mean?

Explanation:

Step1: Analyze the units of the y - axis

The left - hand graph has a y - axis with values around \(3 - 5\), which is likely a cost - related quantity (in dollars). The right - hand graph has a y - axis with larger values (in the hundreds), which is likely a calorie - related quantity.

Step2: Check for proportionality

For a proportional relationship, the ratio \(\frac{y}{x}\) (where \(x\) is volume and \(y\) is the other quantity) should be constant.

• For the left - hand graph (cost vs volume):
• \(\frac{3.75}{10}=0.375\) and \(\frac{4.95}{24}=0.20625\). Since \(0.375

eq0.20625\), it is not proportional.

• For the right - hand graph (calories vs volume):
• \(\frac{150}{10} = 15\) and \(\frac{360}{24}=15\). Since the ratio \(\frac{y}{x}\) is constant (\(k = 15\)).

Step3: Calculate the constant of proportionality

For the right - hand graph (calories vs volume), using the formula \(y=kx\) (proportional relationship). Taking the point \((10,150)\), \(k=\frac{y}{x}=\frac{150}{10}=15\). The constant of proportionality \(k = 15\) means that there are 15 calories per ounce.

Answer:

a. The left - hand graph is “cost vs volume” and the right - hand graph is “calories vs volume”.
b. Calories and volume appear to be in a proportional relationship. We know this because for the right - hand graph (calories vs volume), the ratio \(\frac{\text{calories}}{\text{volume}}\) is constant (\(\frac{150}{10}=\frac{360}{24} = 15\)).
c. The constant of proportionality is \(k = 15\). This number means that there are 15 calories per ounce.