Question

After working for a few years, the instructor has $3,500 saved for rent. He rents an apartment that costs $275 a month. Which graph represents the equation of the scenario?
A graph has month on the x-axis and saved (money) on the y-axis. Points are at (0, 350), (1, 700), (2, 800), (3, 1000), (4, 1,400).
A graph has month on the x-axis and saved (money) on the y-axis. Points are at (1, 3500), (2, 3,000), (3, 2,800), (4, 2,700).
A graph has month on the x-axis and saved (money) on the y-axis. Points are at (0, 3,500), (1, 3,200), (2, 29,00), (3, 2,600), (4, ,300).
A graph has month on the x-axis and saved (money) on the y-axis. Points are at (1, 350), (2, 700), (3, 900), (4, 1200).

Answer 1

The instructor starts with $3,500 in savings and spends $275 each month on rent. After each month, his savings will decrease by $275.

To represent this mathematically, the equation for the savings after \( x \) months can be expressed as:

\[
\text{savings} = 3500 - 275x
\]

Now, let's calculate the savings for the first few months to identify the correct graph:

- At month 0:
\[
\text{savings} = 3500 - 275(0) = 3500
\]

- At month 1:
\[
\text{savings} = 3500 - 275(1) = 3500 - 275 = 3225
\]

- At month 2:
\[
\text{savings} = 3500 - 275(2) = 3500 - 550 = 2950
\]

- At month 3:
\[
\text{savings} = 3500 - 275(3) = 3500 - 825 = 2675
\]

- At month 4:
\[
\text{savings} = 3500 - 275(4) = 3500 - 1100 = 2400
\]

Now we can list the points for the graph:

- Month 0: (0, 3500)
- Month 1: (1, 3225)
- Month 2: (2, 2950)
- Month 3: (3, 2675)
- Month 4: (4, 2400)

Looking through the options provided:

1. The first graph shows points that do not start at $3,500.
2. The second graph starts with $3,500 but has incorrect values.
3. The third graph starts at $3,500 and has the correct subsequent savings amounts.
4. The fourth graph does not fit the money-saving scenario.

Therefore, **the third graph** is the one that represents the equation of the scenario correctly with the points (0, 3500), (1, 3225), (2, 2950), (3, 2675), (4, 2400).