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?
the monthly charge for A is clearly 14.45 (0 minutes)
So, for B, $(22.10-14.45)/45min = $0.17/min
So B s correct answer?
Raj is deciding between two cell phone plans, A and B, which are both linear functions. The monthly charge for plan A according to the number of minutes used is shown in the table.
Monthly Charge for Plan A
Minutes used, x
Monthly charge ($), 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 the linear function that represents the cost of plan B, we can use the formula for the slope of a line:
slope = (change in y) / (change in x)
In this case, the change in y represents the change in the monthly charge and the change in x represents the change in the number of minutes used.
From the given information, we know that the base monthly charge is the same for both plans A and B, so the y-intercept for both plans would be the same. We are only given information about plan B for 45 minutes, so let's use that as our first point of reference.
Point for Plan B: (x1 = 45, y1 = 22.10)
To calculate the slope, we need another point. From the table for Plan A, we can see that for every 3 minutes, the monthly charge increases by $0.39.
So, let's choose another point on Plan B using the same interval of 3 minutes.
Point for Plan B (x2 = 48, y2 = y1 + (0.39 * (48 - 45)))
Now we have two points: (45, 22.10) and (48, y2).
Substituting these values into the slope formula:
slope = (change in y) / (change in x)
slope = (y2 - y1) / (x2 - x1)
slope = (y2 - 22.10) / (48 - 45)
To calculate y2, we substitute x2 = 48 into the linear function for plan B:
y2 = 14.45 + m * 48 (where m is the slope)
Substituting the given values into the equation:
22.10 = 14.45 + m * 48
Solving this equation for m (the slope) will give us the answer.