Question

(05.01)Neil has been running a tutoring business since 2005. He charges a monthly fee for weekly tutoring sessions and a phone help line. Each year, he has increased his fee by the same amount. The table shows what Neil charged each customer for two given years of his business:YearAnnual Tutoring Fee2005$12002008$1350A. What is the rate of change and initial value for Neil’s business? How do you know?B. Write an equation in slope-intercept form to represent the fees that Neil charges each year.

Answer 1

Solution:

Given that, the initial year (2005), the tutoring fee is $1200. Three years later (2008), the tutoring fee is $1350.

Thus, the rate of change, m, is;

$\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ x_1=0,y_1=1200,x_2=3,y_2=1350 \end{gathered}$$\begin{gathered} m=\frac{1350-1200}{3-0} \\ \\ m=\frac{150}{3} \\ \\ m=50 \end{gathered}$

Then, the rate of change for Neil's business is 50 and the initial value is $1200.

(b) The slope-intercept form is written as;

$\begin{gathered} y=mx+b \\ \\ \text{ Where }m\text{ is the rate of change, }b\text{ is the initial value;} \\ y\text{ is the annnua tutoring fee,}x=year \end{gathered}$

ANSWER:

$y(x)=50x+1200$