Question

I need help with this problem and a detailed explanation Option 3.

Answer 1

Constant of proportionality = 1.25

Equation: y = 1.5x

Table:

Cups Price

8 $10

10 $12.5

12 $15

14 $17.5

Step-by-step explanation:

Option 3 says that Micah sold 8 cups of hot cocoa for $10.

First, we need to identify the constant of proportionality. This constant can be calculated as the division of the price by the number of cups, so the constant of proportionality k is equal to:

`\frac{Price}{Number\text{ of cups}}=\frac{\text{ \$10}}{8\text{ cups}}=\text{ \$1.25 per cup}`

The constant of proportionality tells us the price per unit.

Then, we can write the equation that describes a proportional relationship as:

y = kx

Where k is the constant of proportionality, x is the number of cups and y is the price. So, the equation or rule is:

y = 1.25x

Now, we can fill the table using the equation as follows:

Cups Price

8 1.25(8) = $10

10 1.25(10) = $12.5

12 1.25(12) = $15

14 1.25(14) = $17.5

Finally, we can make the graph as follows: