Question

fred hires trident electrik company to install a new light fixture. the electric company will charge an initial fee for the service call. in addition, the total cost of the job includes an installation fee that will depend on how long the job takes. this situation can be modeled as a linear relationship. graph: x-axis time (hours) from 0 to 5, y-axis total cost from $25 to $250, line with y-intercept at (0,25) and passing through (5,225) what does the y-intercept of the line tell you about the situation? options: after the initial fee, fred will pay $40 per hour. including the initial fee, fred will pay $225 if the job takes 5 hours. the initial fee for the service call is $25.

Explanation:

Step1: Recall y - intercept definition

The y - intercept of a linear equation \(y = mx + b\) (where \(m\) is the slope and \(b\) is the y - intercept) occurs when \(x = 0\). In the context of this problem, the \(x\) - axis represents time (in hours) and the \(y\) - axis represents total cost. When \(x = 0\), it means the time spent on the job is 0 hours (i.e., just the service call, no installation time yet).

Step2: Analyze the graph's y - intercept

Looking at the graph, when \(x = 0\) (time = 0 hours), the value of \(y\) (total cost) is \(\$25\). This means that when the job takes 0 hours (only the service call, no installation), the cost is \(\$25\). So this \(\$25\) is the initial fee for the service call.
Now let's analyze the other options:

• "After the initial fee, Fred will pay \$40 per hour." This describes the slope (rate of change per hour), not the y - intercept.
• "Including the initial fee, Fred will pay \$225 if the job takes 5 hours." This is a point on the line (\(x = 5,y = 225\)), not the y - intercept.

Answer:

The initial fee for the service call is \$25.