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.

Answer 1

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.