Question

question 14 3-4 cw
loans the graph shows the amount of money that makena owes after borrowing money to buy a phone. use the graph to estimate the x - and y-intercepts of the function, where the function is positive and negative, and interpret the meanings in the context of the situation.
graph: x-axis is time (months) from 0 to 13, y-axis is amount owed ($) from 0 to 400, a line from (0, 400) to (10, 0)
the x-intercept is select choice. this means that makena will have paid back the money she borrowed after select choice months.
the y-intercept is select choice. this means that makena borrowed $ select choice.
the function is select choice. this means that it takes makena select choice months to pay back the loan.
the graph shows that the function is select choice.

Explanation:

Step1: Find x - intercept

The x - intercept is the point where the graph crosses the x - axis (where the amount owed is $0$). From the graph, we can see that the line crosses the x - axis at $x = 10$. So the x - intercept is the point $(10,0)$, and the x - value of the x - intercept is $10$. This means that Makena will have paid back the money she borrowed after $10$ months.

Step2: Find y - intercept

The y - intercept is the point where the graph crosses the y - axis (where time $x = 0$). From the graph, when $x = 0$, the amount owed $y=400$. So the y - intercept is $(0,400)$, and the y - value of the y - intercept is $400$. This means that Makena borrowed $\$400$.

Step3: Analyze the function's sign and behavior

The function (amount owed as a function of time) is positive when $0\leq x<10$ (because the amount owed is greater than $0$ before she pays off the loan) and zero at $x = 10$. The function is a linear function with a negative slope (since the amount owed decreases as time increases), so it is decreasing. It takes her $10$ months to pay back the loan. The function is positive for $0\leq x<10$ (since amount owed is positive when she still owes money) and zero at $x = 10$.

Answer:

s:

• The x - intercept is $\boldsymbol{(10,0)}$. This means that Makena will have paid back the money she borrowed after $\boldsymbol{10}$ months.
• The y - intercept is $\boldsymbol{(0,400)}$. This means that Makena borrowed $\boldsymbol{\$400}$.
• The function is $\boldsymbol{\text{decreasing}}$. This means that it takes Makena $\boldsymbol{10}$ months to pay back the loan.
• The graph shows that the function is $\boldsymbol{\text{positive for } 0\leq x < 10 \text{ and zero at } x = 10}$ (or we can say positive when she still owes money, i.e., before 10 months and zero when paid off).