The constant of proportionality for the amount of electricity in kilowatt hours and the cost per kilowatt hour is $0.11. Which graph models this situation?

Question

A line graph titled Electricity Cost has Kilowatt hours on the x-axis and Cost in dollars on the y-axis. 100 Kilowatt hours is 11 dollars; 250, 27 dollars and 50 cents.
A line graph titled Electricity Cost has Kilowatt hours on the x-axis and Cost in dollars on the y-axis. 100 Kilowatt hours is 9 dollars; 250, 22 dollars and 50 cents.
A line graph titled Electricity Cost has Kilowatt hours on the x-axis and Cost in dollars on the y-axis. 100 Kilowatt hours is 12 dollars; 250, 30 dollars.
A line graph titled Electricity Cost has Kilowatt hours on the x-axis and Cost in dollars on the y-axis. 100 Kilowatt hours is 13 dollars; 250, 32 dollars and 50 cents.

Answer 1

To determine which graph models the situation with a constant of proportionality of $0.11 per kilowatt hour, we need to calculate the cost for specific amounts of kilowatt hours using this constant.

1. Calculate the cost for 100 kilowatt hours: \[ \text{Cost} = \text{Kilowatt hours} \times \text{Cost per kilowatt hour} = 100 \times 0.11 = 11 \text{ dollars} \]

2. Calculate the cost for 250 kilowatt hours: \[ \text{Cost} = 250 \times 0.11 = 27.50 \text{ dollars} \]

Now we can match these results to the options provided:

• Option 1: 100 kilowatt hours is $11; 250 kilowatt hours is $27.50. (This is correct)
• Option 2: 100 kilowatt hours is $9; 250 kilowatt hours is $22.50. (Incorrect)
• Option 3: 100 kilowatt hours is $12; 250 kilowatt hours is $30. (Incorrect)
• Option 4: 100 kilowatt hours is $13; 250 kilowatt hours is $32.50. (Incorrect)

Therefore, the correct graph that models this situation is the first option.