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\begin{tabular}{|r|r|}
\hline [tex]$x$[/tex] & Balance \\
\hline 0 & [tex]$\$[/tex] 8,000[tex]$ \\
\hline 1 & $[/tex]\[tex]$ 7,888$[/tex] \\
\hline 2 & [tex]$\$[/tex] 7,775[tex]$ \\
\hline 3 & $[/tex]\[tex]$ 7,661$[/tex] \\
\hline 4 & [tex]$\$[/tex] 7,547[tex]$ \\
\hline 5 & $[/tex]\[tex]$ 7,432$[/tex] \\
\hline 6 & [tex]$\$[/tex] 7,316[tex]$ \\
\hline 7 & $[/tex]\[tex]$ 7,200$[/tex] \\
\hline 8 & [tex]$\$[/tex] 7,083[tex]$ \\
\hline 9 & $[/tex]\[tex]$ 6,966$[/tex] \\
\hline 10 & [tex]$\$[/tex] 6,848[tex]$ \\
\hline 11 & $[/tex]\[tex]$ 6,729$[/tex] \\
\hline 12 & [tex]$\$[/tex] 6,609[tex]$ \\
\hline
\end{tabular}

According to the line of best fit, Sean can estimate that the balance of his loan will reach $[/tex]\[tex]$ 0$[/tex] in month [tex]$\square$[/tex].



Answer :

GinnyAnswer
To determine the month when the balance of Sean's loan will reach [tex]$0, we will follow these steps: ### Step 1: Define the Linear Relationship The balance of the loan decreases over time in a linear fashion. This can be described by the formula for a straight line: \[ y = mx + c \] Where: - \( y \) is the loan balance - \( m \) is the slope of the line (rate of change of the balance per month) - \( x \) is the number of months - \( c \) is the y-intercept (initial balance at month 0) ### Step 2: Calculate the Slope (m) and Intercept (c) The slope (\( m \)) indicates the monthly change in the loan balance, and the intercept (\( c \)) represents the starting loan balance at month 0. From the given data, the calculations provide: - Slope \( m = -115.90109890109868 \) - Intercept \( c = 8007.252747252745 \) ### Step 3: Determine the Month when Balance is $[/tex]0
To find out when the balance reaches [tex]$0, we set \( y \) to 0 and solve for \( x \): \[ 0 = -115.90109890109868 \times x + 8007.252747252745 \] Rearrange the equation to solve for \( x \): \[ 115.90109890109868 \times x = 8007.252747252745 \] \[ x = \frac{8007.252747252745}{115.90109890109868} \] ### Step 4: Calculate the Value for x \[ x \approx 69.08694415473606 \] ### Step 5: Interpret the Result The balance of Sean's loan will reach $[/tex]0 after approximately 69 months.

### Final Answer
According to the line of best fit:
- Sean can estimate that the balance of his loan will reach [tex]$0 in month \( 69.08694415473606 \). Thus, the complete answer to the question is: According to the line of best fit and using the given data, Sean can estimate that the balance of his loan will reach $[/tex]0 in month 69.

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