Question

an electrician charges a set fee for every house call and then charges an hourly rate depending on how long the job takes. the total cost of the electricians services can be determined using the equation $c = 65t + 105$, where $t$ is the number of hours the electrician spends at the house working. what is the $y$-intercept of the equation and what is its interpretation in the context of the problem? answer attempt 1 out of 2 the $y$-intercept of the function is which represents

Explanation:

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

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

Step2: Identify the \(y\) - intercept in the given equation

The given equation is \(C = 65t+105\). Comparing it with \(y = mx + b\) (here \(C\) is like \(y\) and \(t\) is like \(x\)), the \(y\) - intercept \(b = 105\).

Step3: Interpret the \(y\) - intercept in the context

When \(t = 0\) (i.e., the electrician spends \(0\) hours at the house working), \(C=65\times0 + 105=105\). So it represents the set fee (the cost when no time is spent on the job) for the house call.

Answer:

The \(y\) - intercept of the function is \(105\) which represents the set fee for the house call.