A college student receives an interest-free loan of $10,200 from a relative. The student will repay $200 per month until the loan is paid off.

a) Express the amount P (in dollars) remaining to be paid in terms of time t (in months). (Give your answer in slope-intercept form.)

b) After how many months will the student owe $5000?

a)

P(t) = 10,200 - 200 t

P(t) = - 200 t + 10,200

b)

Replace P(t) = 5,000 in this equation

5,000 = - 200 t + 10,200

t = 26 months

a) Well, let's break it down. The student borrows $10,200 and repays $200 per month. So, the amount remaining to be paid, P, can be expressed as:

P = 10200 - 200t

Where t is the number of months.

b) So, we want to find out when P (the amount remaining to be paid) will be equal to $5000. Let's substitute that into our equation:

5000 = 10200 - 200t

Now let's solve for t:

200t = 10200 - 5000
200t = 5200
t = 5200/200
t = 26

So, the student will owe $5000 after 26 months.

a) To find the amount remaining to be paid, P, in terms of time, t, we can start with the initial loan amount of $10,200 and subtract the amount repaid each month, which is $200.

The slope-intercept form of an equation is given by: y = mx + b, where m is the slope and b is the y-intercept.

In this case, the slope, m, represents the amount repaid per month ($200), and the y-intercept, b, represents the initial loan amount ($10,200).

Therefore, we can express the amount remaining to be paid, P, in terms of time, t, as:

P = -200t + 10,200

b) To find the number of months it takes for the student to owe $5000, we can set P equal to $5000 and solve for t.

Substituting P = $5000 into the equation from part (a):

5000 = -200t + 10,200

To solve for t, we can isolate the variable by subtracting 10,200 from both sides:

-5200 = -200t

Then, divide both sides by -200:

t = (-5200) / (-200)

Simplifying, we get:

t = 26

Hence, it will take the student 26 months to owe $5000.

To express the amount P (in dollars) remaining to be paid in terms of time t (in months), we can start by analyzing the information given. The student received a loan of $10,200 and is repaying $200 per month.

a) The loan amount remaining to be paid decreases by $200 each month. So, we can express the remaining loan amount, P, as:

P = 10,200 - 200t

In this equation, "t" represents the number of months that have passed since the loan was taken. This equation is in slope-intercept form, y = mx + b, where "m" is the slope (-200 in this case) and "b" is the y-intercept (10,200).

b) To find out after how many months the student will owe $5000, we can substitute P = 5000 into the equation and solve for t:

5000 = 10,200 - 200t

To isolate "t", we can subtract 10,200 from both sides:

-5200 = -200t

Now, divide both sides by -200:

t = -5200 / -200

Simplifying further:

t = 26

Therefore, the student will owe $5000 after 26 months.