1. a lawyer charges $250 per hour to write a legal document, plus $400 for an initial consultation.\na…

Answer:

a. Let $C(n)$ be the total cost and $n$ be the number of hours. The function is $C(n)=250n + 400$. b. We set $C(n)=4650$. So, [ \begin{align*} 250n+400&=4650\ 250n&=4650 - 400\ 250n&=4250\ n&=\frac{4250}{250}\ n& = 17 \end{align*} ] c. The function $C(n)=250n + 400$ is a linear - function in the form $y = mx + b$, where $m = 250$ (the slope) and $b = 400$ (the vertical intercept).

• The vertical intercept is the point $(0,400)$ since when $n = 0$ (no hours of writing the legal document), the cost is just the initial consultation fee of $$400$.
• To find the point of intersection for the solution of part b, we know when $n = 17$, $C(17)=4650$, so the point is $(17,4650)$. Sketch a straight - line passing through the points $(0,400)$ and $(17,4650)$. Label the point $(0,400)$ as the vertical intercept and $(17,4650)$ as the solution point.

Explanation:

Step1: Define the function

The cost has a fixed part ($400$) and a variable part ($250$ per hour). So $C(n)=250n + 400$.

Step2: Solve for $n$

Set $C(n)=4650$ and isolate $n$. First, subtract 400 from both sides: $250n=4650 - 400=4250$. Then divide by 250: $n=\frac{4250}{250}=17$.

Step3: Sketch the line

Identify the vertical intercept from the $y -$intercept of the linear function $y = 250x+400$ which is $(0,400)$. The solution point from part b is $(17,4650)$. Draw a line through these two points.