A phone company has a monthly data plan where a customer pays flat monthly fee of $30 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 $42. If the customer uses 8 GB, the monthly cost will be $62.

a. Find a linear equation for the monthly cost of the data plan as a function of x, the number of MB used.

b. Interpret the slope and y-intercept of the equation.

c. Use your equation to find the total monthly cost if 10 GB are used.

cost=30+rate*volume

42=30+ rate*3
62=30+rate*8

use either equation to solve for rate. Your teacher is too easy.
a) above
b) the slope says more data, more cost. y intercept? Zero data cost

a. Let's first convert the given data from GB to MB. 1 GB = 1024 MB. So, if a customer uses 3 GB, that is equivalent to 3 * 1024 = 3072 MB. And if a customer uses 8 GB, that is equivalent to 8 * 1024 = 8192 MB.

We can now find the linear equation for the monthly cost. Let C be the monthly cost in dollars and x be the number of MB used.

For 3072 MB, the monthly cost is $42. This gives us one point on the line: (3072, 42).

For 8192 MB, the monthly cost is $62. This gives us another point on the line: (8192, 62).

Using these two points, we can find the equation of the line in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

First, let's find the slope m:
m = (y2 - y1) / (x2 - x1)
m = (62 - 42) / (8192 - 3072)
m = 20 / 5120
m = 1/256

Now, let's find the y-intercept b by substituting one of the points into the slope-intercept form:
42 = (1/256) * 3072 + b
42 = 12 + b
b = 42 - 12
b = 30

Thus, the linear equation for the monthly cost of the data plan as a function of x is:
C = (1/256)x + 30

b. The slope of the equation, 1/256, represents how much the monthly cost increases per MB used. In this case, for every additional MB used, the monthly cost increases by 1/256 of a dollar.

The y-intercept of the equation, 30, represents the flat monthly fee of $30. This is the monthly cost when no data (0 MB) is used.

c. To find the total monthly cost if 10 GB (10240 MB) are used, we can substitute x = 10240 into the equation:
C = (1/256)(10240) + 30
C = 40 + 30
C = 70

Therefore, the total monthly cost if 10 GB are used is $70.

a. To find the linear equation for the monthly cost of the data plan, we need to determine the rate at which the cost increases for each additional GB of data used.

Let's denote the monthly cost as C and the number of GB used as x. We know that the cost for using 3 GB is $42 and the cost for using 8 GB is $62. With this information, we can find the slope and y-intercept of the linear equation.

We can use the two points (3, 42) and (8, 62) to find the slope (m):

m = (y2 - y1) / (x2 - x1)
m = (62 - 42) / (8 - 3)
m = 20 / 5
m = 4

So the slope of the linear equation is 4.

To find the y-intercept (b), we can substitute one of the points into the equation and solve for b. Let's use the point (3, 42):

42 = 4 * 3 + b
42 = 12 + b
b = 30

So the y-intercept of the linear equation is 30.

Therefore, the linear equation for the monthly cost (C) as a function of the number of GB used (x) is:

C = 4x + 30

b. The slope (4) represents the additional cost per GB of data used. In other words, for every additional GB of data used, the monthly cost increases by $4.

The y-intercept (30) represents the fixed monthly cost that the customer pays regardless of the amount of data used. Even if the customer doesn't use any data, they still need to pay the flat fee of $30.

c. To find the total monthly cost if 10 GB are used, we can substitute x = 10 into the equation:

C = 4 * 10 + 30
C = 40 + 30
C = 70

So the total monthly cost for using 10 GB would be $70.

To solve this problem, we need to determine the linear equation that represents the relationship between the monthly cost and the amount of data used.

a. To find the equation, we can use the given information about the monthly cost for different amounts of data used. Let's denote the monthly cost as C and the number of GB used as x.

From the problem, we have two points: (3, 42) and (8, 62). These points represent the number of GB used and the corresponding monthly cost.

Using the two points to find the equation of the line, we can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.

Slope (m) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)

Using the points (3, 42) and (8, 62):
m = (62 - 42) / (8 - 3)
m = 20 / 5
m = 4

The y-intercept (b) can be obtained by substituting the values of one of the points into the equation:
42 = 3(4) + b
42 = 12 + b
b = 42 - 12
b = 30

The linear equation that represents the monthly cost of the data plan as a function of x (number of GB used) is:
C = 4x + 30

b. The slope of the equation, 4, represents the additional cost per GB used. This means that for each additional GB used, the monthly cost increases by $4.

The y-intercept of the equation, 30, represents the flat monthly fee. This means that even if the customer uses 0 GB of data, they will still have to pay a base fee of $30.

c. To find the total monthly cost if 10 GB is used, we can substitute x = 10 into the equation:
C = 4(10) + 30
C = 40 + 30
C = 70

Therefore, the total monthly cost for using 10 GB would be $70.