A phone company has a monthly data plan where a customer pays flat monthly fee of $20 and then a certain amount of money per gigabyte (GB) of data used on the phone. If a customer uses 3 GB, the monthly cost will be
$26. If the customer uses 4 GB, the monthly cost will be $28.
a. Find a linear equation for the monthly cost of the data plan as a function of
x, the number of MB used.
C(x) =
b. Interpret the slope and y-intercept of the equation.
From the first part of your data, we know that
C(x) = mx + 20
we know 2 ordered pairs (3,26) and (4,28)
sub in the first:
26 = 3m+20
3m = 6
m = 2
so C(x) = 2x + 20
Did you notice that the 2nd point was not needed, thus the part "If the customer uses 4 GB, the monthly cost will be $28" is superfluous information.
Use you knowledge about the equation in the form y = mx + b to answer b)
a. The linear equation for the monthly cost of the data plan can be determined using the given information. We know that when the customer uses 3 GB, the monthly cost is $26, and when the customer uses 4 GB, the monthly cost is $28. Let's convert GB into MB, as 1 GB = 1000 MB.
When the customer uses 3 GB = 3000 MB, the monthly cost is $26.
When the customer uses 4 GB = 4000 MB, the monthly cost is $28.
Now, let's calculate the increase in cost per MB.
Change in cost = $28 - $26 = $2
Change in data usage = 4000 MB - 3000 MB = 1000 MB
So, the increase in cost per MB = $2 / 1000 MB = $0.002 per MB.
Now, let's find the fixed monthly cost.
At 3000 MB, the monthly cost is $26. Using the slope and the data, we can find the fixed fee.
x = 3000 MB
y = $26
slope (m) = $0.002
Using the slope-intercept form of a linear equation (y = mx + b):
$26 = $0.002 * 3000 MB + b
$26 = $6 + b
b = $26 - $6
b = $20
So, the equation for the monthly cost of the data plan as a function of x, the number of MB used, is:
C(x) = $0.002x + $20
b. The slope of the equation, $0.002, represents the increase in cost per MB used. In other words, it shows how the monthly cost changes for each additional MB of data used.
The y-intercept of the equation, $20, represents the fixed monthly fee that the customer has to pay regardless of their data usage. It is the starting point for the monthly cost of the data plan.
To sum it up humorously:
The slope is like a slippery hill that signifies how much your monthly cost increases as you slide down the data usage mountain. The y-intercept is like a cozy base camp where you pay your fixed fee and rest comfortably, even if you don't venture far into the data wilderness.
a. To find a linear equation for the monthly cost as a function of the number of GB used, we need to find the equation of the line passing through the points (3, 26) and (4, 28).
Let x represent the number of GB used, and C(x) represent the monthly cost.
Using the point-slope form of a linear equation, we can start by finding the slope:
slope = (change in y) / (change in x) = (28 - 26) / (4 - 3) = 2 / 1 = 2
Now, we can use the slope-intercept form of a linear equation to find the y-intercept:
y - y1 = m(x - x1)
Taking the point (3, 26):
y - 26 = 2(x - 3)
Expanding the equation:
y - 26 = 2x - 6
Now, we can solve for y:
y = 2x - 6 + 26
y = 2x + 20
So, the linear equation representing the monthly cost of the data plan as a function of x, the number of GB used, is:
C(x) = 2x + 20
b. The slope of the equation, 2, represents the additional cost per gigabyte. It indicates that for every additional GB used, the monthly cost increases by $2.
The y-intercept of the equation, 20, represents the base monthly fee. It indicates that even if no GB is used, the customer still needs to pay a flat fee of $20.
a. To find the linear equation for the monthly cost of the data plan, we can use the given information and form two ordered pairs, (3, 26) and (4, 28), where the first number represents the number of GB used and the second number represents the monthly cost.
We can use the slope-intercept form of a linear equation, which is given by y = mx + b, where y is the dependent variable (monthly cost), x is the independent variable (number of GB used), m is the slope, and b is the y-intercept.
Let's find the slope first:
m = (y2 - y1) / (x2 - x1)
m = (28 - 26) / (4 - 3)
m = 2 / 1
m = 2
Now we can substitute one of the ordered pairs in the equation to find the y-intercept:
26 = 2 * 3 + b
26 = 6 + b
b = 26 - 6
b = 20
Therefore, the linear equation for the monthly cost of the data plan is:
C(x) = 2x + 20
b. The slope of the equation, which is 2, represents the additional cost per GB of data used. The y-intercept, which is 20, represents the fixed monthly fee of $20.
In other words, for every additional GB used, the monthly cost increases by $2. The y-intercept of 20 means that even if the customer doesn't use any data (x = 0), they will still have to pay the fixed monthly fee of $20.