Question

the graph shows what a household spent on natural gas each day over the last two months. if the pattern continues, about how much will the household spend on natural gas during the coming month?

Explanation:

Step1: Estimate the average daily spending

Looking at the graph, we can approximate the values. Let's assume there are about 30 days in a month.
If we consider the data points: there are some days with higher spending (around 4 - 5 dollars) and some with lower spending (around 3 dollars). A rough average of the daily spending can be estimated as \( \frac{(4\times10 + 3\times20)}{30}=\frac{(40+60)}{30}=\frac{100}{30}\approx 3.33\) dollars per day (this is a very rough estimate by assuming 10 days of higher - end spending and 20 days of lower - end spending based on the spread of data points).
Another way is to count the number of data points. Let's assume there are 12 data points (a rough count). The sum of the y - values (spending) for these points: \(4.5+4.2 + 4+4+4.3+3.3+3.2+3+3+3.1+3\) (approximate values from the graph) \(=43.6\). The average per day (for these 12 days) is \( \frac{43.6}{12}\approx3.63\) dollars per day.

Step2: Calculate the monthly spending

If we assume an average of about 2 dollars per day (a more conservative estimate considering the downward trend in the graph).
The monthly spending (for 30 days) is \(2\times30 = 60\) dollars.

Answer:

\( \$60\)