Question

two electricians, electrician a and electrician b, offer pricing plans for their work. each electrician charges an initial fee for a service call plus an hourly rate. the charges for each electrician are represented by the equation and the table shown below.
electrician a
c = 25x + 50
electrician b
which statement comparing the charges for each electrician is true?
a electrician a has an initial fee and an hourly rate that are both less than those for electrician b.
b electrician a has an initial fee and an hourly rate that are both greater than those for electrician b.
c electrician a has an initial fee that is less than that for electrician b. the hourly rate for electrician a is greater than that for electrician b.
d electrician a has an initial fee that is greater than that for electrician b. the hourly rate for electrician a is less than that for electrician b.

Explanation:

Step1: Find the equation for Electrician B

The formula for a linear equation is \(y = mx + b\), where \(m\) is the slope (hourly rate) and \(b\) is the \(y\) - intercept (initial fee).
The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using the points \((x_1 = 3,y_1=130)\) and \((x_2 = 4,y_2 = 150)\)
\(m=\frac{150 - 130}{4 - 3}=\frac{20}{1}=20\)
Substitute \(m = 20\) and \((x = 3,y = 130)\) into \(y=mx + b\)
\(130=20\times3 + b\)
\(130 = 60 + b\)
\(b=130 - 60=70\)
The equation for Electrician B is \(C = 20x+70\)

Step2: Compare initial fees and hourly rates

For Electrician A: The equation is \(C = 25x + 50\), so the hourly rate \(m_A=25\) and the initial fee \(b_A = 50\)
For Electrician B: The equation is \(C = 20x+70\), so the hourly rate \(m_B=20\) and the initial fee \(b_B = 70\)

Since \(b_A=50<70 = b_B\) (initial fee of A is less than B) and \(m_A = 25>20=m_B\) (hourly rate of A is greater than B)

Answer:

C. Electrician A has an initial fee that is less than that for Electrician B. The hourly rate for Electrician A is greater than that for Electrician B.