Question

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?
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.