Henry took a loan from the bank. D represents Henry’s remaining debt (in $) after T months. D= -200T + 9000. What do the slope and D-intercept represent and what is the rate of change?

Answer 1

This problem requires knowledge of graphing equations and using slope and y intercept knowledge.

Here is the above equation...

D = -200T+9000

D = 'Debt'

T = Time(in months)

From a general analysis we can look at the time as decreasing the debt as stated in the initial question. If we want to find the debt intercept for this equation we can simple set T = 0. Setting T equal to 0 finds the y-intercept or D-intercept if your would like to label your graph the generic (X,Y) or (T,D)

D = -200(0) + 9000 = 9000$ #here is the debt intercept which represents the initial debt when Henry begins to work off his loan.

Next, we can begin to think more about the -200 and what it means when we are using time and months to count the total debt.

Try using the T values... T = 0, 1, 2, 3 and find the relationship between time and the change in debt.

T | D

0 | 9000

1 | 8800

2 | 8600

3 | 8400

By plugging in the values, you will be able to denote the trend in the decrease of debt being 200$ per month. This can be directly pointed to the slope(or number multiplied with the variable in the debt equation.

D = -200T +9000

Answer 2

Hello, Sea,

The equation D = -200T + 9000

can be rephrased using my friends x and y and set up in a standard format of

y = mx + b

It makes it easier for me to see what is happening.

y = -200x + 900

Now we see the slope, or rate of change, is -200 and we lose the "D- intercept nonsense" and call it the y-intercept now. which I see is 900.

The slope, -200, is the rate at which the loan is being paid off, which is $200/month

The y-intercept is 900, which is the value at t = 0, or the start of the loan. So the loan was for $900.

Bob