Question

an electrician charges a set fee for every house call and then charges an hourly rate depending on how long the job takes. let c represent the total cost of visit when the electrician spends t hours at the house working. a graph of c is shown below. write an equation for c then state the slope of the graph and determine its interpretation in the context of the problem.
answer attempt 1 out of 2
c = 50t + 100
the slope of the function is 50 which represents

Explanation:

Step1: Determine the slope - intercept form of a linear equation

The slope - intercept form of a linear equation is \(C = mt + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept.

Step2: Find the \(y\) - intercept

When \(t = 0\) (no hours of work), from the graph, \(C=100\). So \(b = 100\).

Step3: Calculate the slope

We can use two points on the line. Let's assume two points \((t_1,C_1)=(0,100)\) and \((t_2,C_2)=(5,350)\).
The slope formula is \(m=\frac{C_2 - C_1}{t_2 - t_1}\).
Substitute \(C_1 = 100\), \(t_1 = 0\), \(C_2=350\), \(t_2 = 5\) into the formula:
\(m=\frac{350 - 100}{5-0}=\frac{250}{5}=50\).

Step4: Write the equation

Substitute \(m = 50\) and \(b = 100\) into \(C=mt + b\).
We get \(C = 50t+100\).

Answer:

The equation for \(C\) is \(C = 50t + 100\). The slope of the graph is \(50\), which represents the hourly rate charged by the electrician.