Question

The scatter plot shows the balance of a loan over the course of two years. Assuming the line of best fit for the given scatterplot is y = -353.71x + 18,075, after how many months will the balance of the loan reach $0? A graph shows Months on the x-axis and Loan Balance in dollars on the y-axis. Dot plotted at (0, 18,000), (1.5, 17,500), (3, 17,000), (4.9, 16,200), (7, 15, 900), (8, 15,000), (9, 14,200), (11, 14,000), (13, 13,900), (14, 13,000). A. 32 months B. 35 months C. 47 months D. 51 months

Answer 1

Using the line of best fit equation y = -353.71x + 18,075, the balance of the loan will reach $0 after approximately 51 months when solving for x with the y-value set to zero.

Step-by-step explanation:

To determine after how many months the balance of the loan will reach $0, we use the equation of the line of best fit y = -353.71x + 18,075. To find the x-value when y is zero (0), we set the equation equal to zero and solve for x (the number of months):

0 = -353.71x + 18,075

To isolate x, we move -353.71x to the other side of the equation:

353.71x = 18,075

Then, divide both sides by 353.71 to solve for x:

x = 18,075 / 353.71

x ≈ 51 months

Therefore, the balance of the loan will reach $0 after approximately 51 months.