Question

an electrician charges $75 per hour on top of a set fee of $100 for every house call. make a table of values and then write an equation for c, in terms of t, representing the total cost of the electricians services if the electrician spends t hours at the house working.

answer attempt 1 out of 2

you must answer all questions above in order to submit.

Explanation:

Step1: Calculate total cost for \(t = 0\)

The set - fee is \(100\). When \(t=0\), \(C=100 + 75\times0=100\)

Step2: Calculate total cost for \(t = 1\)

Using the formula \(C=\text{set - fee}+\text{hourly rate}\times t\). Here, set - fee \( = 100\), hourly rate \(=75\), \(t = 1\). So \(C=100+75\times1=175\)

Step3: Calculate total cost for \(t = 2\)

Using the formula \(C = 100+75t\). Substitute \(t = 2\), we get \(C=100+75\times2=100 + 150=250\)

Step4: Calculate total cost for \(t = 3\)

Using the formula \(C=100 + 75t\). Substitute \(t = 3\), we get \(C=100+75\times3=100+225 = 325\)

Step5: Derive the general equation

The general form of a linear equation is \(y=mx + b\), where \(m\) is the slope (rate of change) and \(b\) is the \(y\) - intercept (initial value). Here, the rate of change \(m = 75\) (cost per hour) and the initial value \(b = 100\) (set - fee). So the equation is \(C=75t + 100\)

Answer:

Number of Hours Working	Total Cost for Electrician Services
\(1\)	\(175\)
\(2\)	\(250\)
\(3\)	\(325\)

The equation is \(C = 75t+100\)