SkyHigh TV is a satellite television provider. They charge by the month. The first month of service costs $85.45. The second month of service costs $148.65. The third month of service costs $211.85. Write an equation in the form of
y = c + d( x −1)
to represent this situation. Explain your answer.
third month - second month = 63.20
second month - first month = 63.20 (remarkable)
so if
x = month number
y = cost for month x
then
cost for month x = y = 85.45 + 63.20 (x-1)
====================
check for month 3
y = 85.45 + 63.2(3-1) = 85.45 + 63.20*2 = 211.85
Wow.
To write an equation in the form of y = c + d(x - 1) to represent this situation, we need to identify the variables and their values.
Let's assign the variable x to represent the number of months of service, and y to represent the cost of service for a particular month.
Given:
First month cost = $85.45 (x = 1, y = $85.45)
Second month cost = $148.65 (x = 2, y = $148.65)
Third month cost = $211.85 (x = 3, y = $211.85)
To find the values of c and d, we can substitute the values of x and y into the equation and solve for c and d.
For the first month:
85.45 = c + d(1 - 1)
85.45 = c
For the second month:
148.65 = c + d(2 - 1)
148.65 = c + d
For the third month:
211.85 = c + d(3 - 1)
211.85 = c + 2d
Since we found that c = 85.45 from the first equation, we can substitute this value into the second and third equations:
148.65 = 85.45 + d (equation 2)
211.85 = 85.45 + 2d (equation 3)
Now we can solve equation 2 for d:
d = 148.65 - 85.45
d = 63.20
Lastly, we can substitute the value of d into equation 3 to solve for c:
211.85 = 85.45 + 2(63.20)
211.85 = 85.45 + 126.40
211.85 = 211.85
Therefore, the equation in the form of y = c + d(x - 1) to represent this situation is:
y = 85.45 + 63.20(x - 1)
This equation allows us to calculate the cost of service for any given month (x) based on the initial cost (c = 85.45) and the additional monthly cost (d = 63.20).
To write an equation in the form of y = c + d(x - 1) to represent the given situation, we need to understand the pattern in the monthly costs.
In this case, the monthly cost appears to be increasing by a fixed amount every month. To find this fixed amount, we can subtract the cost of the first month from the cost of the second month, and then subtract the cost of the second month from the cost of the third month.
First, let's find the increase in cost from the first month to the second month:
148.65 - 85.45 = 63.2
Next, let's find the increase in cost from the second month to the third month:
211.85 - 148.65 = 63.2
We can see that the monthly cost is increasing by $63.2 each month.
Now, we can write the equation in the form of y = c + d(x - 1).
c represents the initial cost, which is the cost in the first month, and d represents the rate of increase.
In this case, the initial cost (c) is $85.45, and the rate of increase (d) is $63.2.
Therefore, the equation to represent this situation would be:
y = 85.45 + 63.2(x - 1)