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?

Question

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).