Raj is deciding between two cell phone plans, A and B, which are both linear functions. The monthly charge for plan A according to the number of minutes used is shown in the table.
Monthly Charge for Plan A
Minutes used, x
Monthly charge ($), y
0
14.45
3
14.84
6
15.23
9
15.62
12
16.01
Plan B has the same monthly base charge as plan A, but it charges a different amount per minute used. If the total monthly charge for plan B is $22.10 when 45 minutes are used, what is the slope of the linear function that represents the cost of plan B?
0.13
0.17
0.39
0.45
To find the slope of a linear function, we can use the formula:
slope = (change in y) / (change in x)
In the table for plan A, we can see that for every 3 additional minutes used, the monthly charge increases by $0.39. This means that the change in y is $0.39 and the change in x is 3.
For plan B, we know that the total monthly charge is $22.10 when 45 minutes are used. We can represent this as a point on the graph: (45, 22.10).
To find the slope for plan B, we need to compare the change in y and change in x. We can subtract the base charge of plan A, 14.45, from the total monthly charge of plan B, 22.10, to find the change in y:
22.10 - 14.45 = 7.65
The change in x is 45 - 0 = 45.
Now we can calculate the slope:
slope = (change in y) / (change in x)
slope = 7.65 / 45
slope = 0.17
So the slope of the linear function that represents the cost of plan B is 0.17.
To find the slope of the linear function that represents the cost of plan B, we need to use the formula for the slope of a line. The formula for slope is:
slope = (change in y) / (change in x)
We can use the given information that plan B has the same base charge as plan A and that the total monthly charge for plan B is $22.10 when 45 minutes are used.
Let's calculate the change in y and change in x for plan B using the given information:
Change in y = Total monthly charge for plan B - Base charge for plan B
Change in y = $22.10 - Base charge for plan B
Change in x = 45 minutes - 0 minutes
Change in x = 45 minutes
Now we can calculate the slope:
slope = (change in y) / (change in x)
slope = ($22.10 - Base charge for plan B) / 45
Since the base charge for plan B is the same as plan A, it will be the same as the monthly charge for plan A when 0 minutes are used. Looking at the table, we see that when 0 minutes are used, the monthly charge for plan A is $14.45.
Substituting this information into the slope equation gives:
slope = ($22.10 - $14.45) / 45
slope = $7.65 / 45
slope ≈ 0.17
Therefore, the slope of the linear function that represents the cost of plan B is approximately 0.17.