High School

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Determine how long it will take to reach the given balances using the best-fit equation \( y = -382.05x + 25,077.40 \).

The table represents the balance of Sylvia’s loan, \( y \), over a period of 24 months, \( x \):
\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
0 & \$25,000 \\
2 & \$24,274 \\
4 & \$23,542 \\
6 & \$22,802 \\
8 & \$22,056 \\
10 & \$21,303 \\
12 & \$20,543 \\
14 & \$19,775 \\
16 & \$19,001 \\
18 & \$18,219 \\
20 & \$17,430 \\
22 & \$16,633 \\
24 & \$15,829 \\
\hline
\end{array}
\]

Using the scatter plot and the best-fit equation, determine:

1. The month the balance of the loan will be approximately \$17,000.
2. The month the balance of the loan will reach \$0.

Tiles:
- month 66
- month 24
- month 21
- month 60

Answer :

Final answer:

To determine when Sylvia's loan balance will reach specific amounts, substitute the given balances into the best-fit equation to find the corresponding months.

Explanation:

Determine how long it will take to reach the given balances:

Given the equation y = -382.05x + 25,077.40, substitute $17,000 for y to find x, which turns out to be approximately month 60.

To find when the loan balance will reach $0, substitute y = 0 into the equation to solve for x, resulting in month 66.

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