The instructor had saved $3,500 and rents an apartment for $275 monthly. He believes the point (6, 1850) would be on the equation of the line. Is he correct? Explain how to check if a point is on a line.

1 answer

To determine if the point (6, 1850) is on the line that represents the instructor's financial situation, we first need to derive the equation of that line.

Let's break it down:

  1. Understanding the situation:

    • The instructor has $3,500 saved.
    • He spends $275 monthly on rent.
  2. Plane context:

    • We can define the x-axis as the number of months (x), and the y-axis as the amount of money remaining (y) after paying the rent.
    • The initial amount saved is $3,500, which means at month 0 (x = 0), y = 3500.
  3. Setting up the equation:

    • After 1 month, the amount left would be: \[ y = 3500 - 275x \]
    • This equation describes how the remaining funds decrease over time due to rent payments.
  4. Checking if the point (6, 1850) is on the line:

    • Plug x = 6 into the equation to see if we get y = 1850: \[ y = 3500 - 275 \cdot 6 \]
    • Calculate: \[ y = 3500 - 1650 = 1850 \]
  5. Conclusion:

    • Since substituting x = 6 into the equation gives us y = 1850, the point (6, 1850) is indeed on the line represented by the equation \( y = 3500 - 275x \).

Thus, the instructor is correct; the point (6, 1850) is on the line that describes his financial situation according to the equation derived.