The relationship described below can be modeled using an equation. Identify the variables and write an equation to solve the questions below.
Number of Credits Fees
3 2000
6 2600
9 3200
12 3800
15 4400
a) Write an equation to calculate the fees F when the number of credits n is given.
b) Use the equation from part (a) to calculate the fee for 17 credits
Graph it if you don't understand my solution:
Linear equations follow the format y=mx+b
where m is the slope and b is the y-intercept.
let y= fees and x=number of credits
now calculate slope (change in y/change in x)
m=(2600-2000)/(6-3)= 200
y=200x+b
Plug in any point to find b
2000=200(3)+b
b=1400
so your equation is y=200x+1400
:P
Looks like a straight line of slope (600/3) to me since fees increase 600 for every three credits.
F = 200 C + b solve for b
2000 = 200 (3) + b
2000 = 600 + b
b = 1400
so
Fee = 200 (Credits) + 1400
check with (15 , 4400)
4400 = (200)(15) + 1400 ?????
4400 = 3000 + 1400 ???? YES, check
Now do
Fee = 200 (17) + 1400 for part b
To find the equation that models the relationship between the number of credits and fees, we need to identify the variables in the data given. In this case, the number of credits (n) is the independent variable, and the fees (F) are the dependent variable.
a) To write an equation to calculate the fees (F) when the number of credits (n) is given, we need to determine the relationship between these two variables. Notice that as the number of credits increases, the fees also increase. Additionally, the increase in fees is not a constant amount. From the data, we can observe that as the number of credits increases by 3, the fees increase by 600.
We can use this information to build an equation. Let's assume that the initial fee for 3 credits is $2000. The additional fee for each extra credit is $200 (600 divided by 3). So, the equation can be written as:
F = 2000 + 200(n - 3)
b) To calculate the fee for 17 credits using the equation above, we substitute n = 17 into the equation:
F = 2000 + 200(17 - 3)
F = 2000 + 200(14)
F = 2000 + 2800
F = 4800
Therefore, the fee for 17 credits would be $4800.