To solve this problem, we need to determine the slope of the linear function that represents the cost of Plan B.
### Step 1: Understand the structure of Plan A
Plan A's costs are given in the table, showing that the cost for Plan A is a linear function of minutes used. In a linear function of the form [tex]\( y = mx + b \)[/tex], [tex]\( m \)[/tex] is the slope (rate per minute) and [tex]\( b \)[/tex] is the y-intercept (base charge).
### Step 2: Calculate the slope ([tex]\(m\)[/tex]) and base charge ([tex]\(b\)[/tex]) of Plan A
The given points from the table for Plan A are (0, 14.45) and (3, 14.84).
- From (0, 14.45), we know that the y-intercept (base charge) [tex]\( b \)[/tex] is 14.45.
- The slope, [tex]\( m_A \)[/tex], can be calculated using the two points (0, 14.45) and (3, 14.84):
[tex]\[
m_A = \frac{(14.84 - 14.45)}{(3 - 0)} = \frac{0.39}{3} = 0.13
\][/tex]
Thus, the linear equation for Plan A is:
[tex]\[ y = 0.13x + 14.45 \][/tex]
### Step 3: Identify the base charge and total charge details of Plan B
Plan B has the same base charge ([tex]\( b \)[/tex]) as Plan A, which is 14.45. Given that the total monthly charge for Plan B with 45 minutes is 22.10, we can use this information to calculate the slope for Plan B.
### Step 4: Calculate the slope ([tex]\( m \)[/tex]) for Plan B
Using the information that the total charge for 45 minutes in Plan B is $22.10, we can set up the equation:
[tex]\[
22.10 = m_B \cdot 45 + 14.45
\][/tex]
To solve for [tex]\( m_B \)[/tex]:
First, subtract the base charge from the total charge:
[tex]\[
22.10 - 14.45 = 7.65
\][/tex]
Then, divide by the number of minutes (45):
[tex]\[
m_B = \frac{7.65}{45} = 0.17
\][/tex]
### Conclusion
The slope of the linear function representing the cost of Plan B is:
[tex]\[ \boxed{0.17} \][/tex]
