Question

shows the function relating javier’s remaining balance to the number of months
time (months) | remaining balance ($)
x | y
0 | 1950
2 | 1300
5 | 325
6 | 0
a. find the intercepts.
the x - intercept is
the y - intercept is
b. describe what the intercepts mean in the context of the situation.
the x - intercept means that after months, javier’s remaining balance will be $
, or it will take javier months to repay his parents.
the y - intercept means that javier owes his parents $ after
months, or javier initially borrowed $ from his parents

Explanation:

Step1: Identify x-intercept

The x-intercept is the x-value when $y=0$. From the table, when $y=0$, $x=6$.

Step2: Identify y-intercept

The y-intercept is the y-value when $x=0$. From the table, when $x=0$, $y=1950$.

Step3: Interpret x-intercept context

The x-intercept corresponds to when the remaining balance is $0$, so it is the time to repay the full amount.

Step4: Interpret y-intercept context

The y-intercept corresponds to the initial amount borrowed, when 0 months have passed.

Answer:

a.
The x-intercept is $\boldsymbol{6}$
The y-intercept is $\boldsymbol{1950}$

b.
The x-intercept means that after $\boldsymbol{6}$ months, Javier's remaining balance will be $\boldsymbol{0}$, or it will take Javier $\boldsymbol{6}$ months to repay his parents.
The y-intercept means that Javier owes his parents $\boldsymbol{1950}$ after $\boldsymbol{0}$ months, or Javier initially borrowed $\boldsymbol{1950}$ from his parents.