Final answer:
A new Audi purchased by Eric is being paid off with monthly payments. The equation in point-slope form is y - 37200 = -545(x - 10). Eric must pay $545 per month. The cost of the Audi when Eric purchased it was $42,650. It will take approximately 79 months to pay off the car entirely. The value of the very last payment Eric must make before it is paid off is approximately $2,045.
Step-by-step explanation:
a. To write the equation in point-slope form, we use the formula: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. We can use the points (10, 37200) and (24, 29570) to find the slope:
m = (29570 - 37200) / (24 - 10) = -7630 / 14 = -545
Using the point-slope form with the point (10, 37200), the equation is: y - 37200 = -545(x - 10)
b. To find the monthly payment, we can set up a linear equation using the slope-intercept form y = mx + b. We can use the point (10, 37200) to find the value of b:
37200 = -545(10) + b
b = 37200 + 5450 = 42650
So the equation in slope-intercept form is: y = -545x + 42650
c. The monthly payment represents the y-value in the equation. So Eric must pay $545 per month.
d. To find the cost of the Audi, we can use the equation in slope-intercept form. When x (the number of payments) is 0, y (the amount owed) represents the cost of the car. So when x = 0, y = -545(0) + 42650 = 42650. Therefore, the Audi cost $42,650 when Eric purchased it.
e. To find the number of months it will take to pay off the car entirely, we can set y (the amount owed) to 0 and solve for x (the number of payments) in the equation in slope-intercept form: 0 = -545x + 42650. Solving for x, we get x = 42650 / 545 ≈ 78.21. So it will take approximately 79 months to pay off the car entirely.
f. The value of the very last payment Eric must make before it is paid off can be found by substituting x = 78 into the equation in slope-intercept form: y = -545(78) + 42650 ≈ $2,045. So the value of the last payment is approximately $2,045.