To find when the balance of Sean's loan will reach [tex]$0, we can use the provided equation for the line of best fit:
\[ y = -115.9x + 8007.30 \]
Here, \( y \) represents the balance of the loan, and \( x \) represents the number of months. To determine when the balance of the loan will be \( \$[/tex]0 \), we need to solve for [tex]\( x \)[/tex] when [tex]\( y \)[/tex] is set to [tex]\( 0 \)[/tex].
Step 1: Set up the equation for when the balance is zero:
[tex]\[ 0 = -115.9x + 8007.30 \][/tex]
Step 2: Solve for [tex]\( x \)[/tex]:
[tex]\[ 115.9x = 8007.30 \][/tex]
[tex]\[ x = \frac{8007.30}{115.9} \][/tex]
Step 3: Calculate the value:
[tex]\[ x \approx 69.088 \][/tex]
Therefore, using the line of best fit, Sean can estimate that the balance of his loan will reach [tex]\( \$0 \)[/tex] in month [tex]\( 69.088 \)[/tex], or approximately the [tex]\( 69^{th} \)[/tex] month.
Final answer:
- According to the line of best fit and using ___[tex]\[ x = \frac{8007.30}{115.9} \][/tex], Sean can estimate that the balance of his loan will reach [tex]\( \$0 \)[/tex] in month ___[tex]\[ 69.088 \][/tex]
