Question

linear functions in context worksheet. john was approved for a car loan with 0% interest rate as long as the balance is paid off in twelve months. the graph represents johns payment plan to ensure that he doesnt have to pay interest. 1. what is the slope of the function? explain its meaning in the context of the scenario. 2. what is the x - intercept of the function? explain its meaning in the context of the scenario. 3. what is the y - intercept of the function? explain its meaning in the context of the scenario. 4. what is the domain of the function? explain its meaning in the context of the scenario.

Explanation:

Step1: Recall slope formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(0,9000)$ and $(x_2,y_2)=(12,0)$.

Step2: Calculate slope

$m=\frac{0 - 9000}{12-0}=\frac{- 9000}{12}=-750$. In the context, it means John pays off $750$ of his car - loan balance per month.

Step3: Find x - intercept

The x - intercept is the value of x when y = 0. From the graph, when the loan balance (y) is 0, the number of months (x) is 12. It means it takes 12 months for John to pay off his car loan.

Step4: Find y - intercept

The y - intercept is the value of y when x = 0. From the graph, when the number of months (x) is 0, the loan balance (y) is 9000. It means John's initial car loan amount is $9000$.

Step5: Determine domain

The domain is the set of all possible x - values. Here, x represents the number of months. Since the loan must be paid off in 12 months, the domain is $0\leq x\leq12$. It means the time period for which the loan - payment plan is applicable is from 0 months (the start) to 12 months (when the loan is fully paid off).

Answer:

1. Slope: - 750. It means John pays off $750 of his car - loan balance per month.
2. x - intercept: 12. It means it takes 12 months for John to pay off his car loan.
3. y - intercept: 9000. It means John's initial car loan amount is $9000.
4. Domain: $0\leq x\leq12$. It means the time period for which the loan - payment plan is applicable is from 0 months (the start) to 12 months (when the loan is fully paid off).