Question

1) a local yoga club has a no conract basic membership plan with an initial fee of $70.00 and a per month charge of $35.00 A) write a liner equation in slope intercept form for the total cost C in dollars of this plain if you countiue your membership for M monthsB) Identify the dependent and independent variable for the linear equation found in part Ac) how many months of membership will $665.00 purchase at this club?

Answer 1

Answer

A. The linear equation in slope-intercept form is

$C=35M+70$

B. The number of months (M) must be the independent variable, and the cost of the membership (C) must be the dependent variable.

C. The number of months of membership that $665.00 will purchase at the club is: 17 months

SOLUTION

Problem Statement

The question tells us a yoga club charges an initial fee of $70.00 and $35.00 per month afterward.

We are asked to find:

A. Find the linear equation in slope-intercept form.

B. Identify the dependent and independent variables for the linear equation

C. How many months of membership will $665.00 purchase at the club?

Method

A. In order to find the slope-intercept form, we need to know the general formula for a slope-intercept form of linear equation.

The general formula is given below as:

$\begin{gathered} C=bM+k \\ \text{where,} \\ C=\text{ Total cost in dollars} \\ b=\text{slope of the equation } \\ M=\text{ Number of Months} \\ k=\text{Initial value of C (also called the y-intercept of the equation)} \end{gathered}$

The question tells us the yoga club charges $70.00 initially. This means that the y-intercept of our equation is:

$k=70$

Next, we are told that the monthly rate charged is $35.00. The rate of any linear equation is the same as the slope (b).

Therefore, the slope is:

$b=35$

This means we can write our slope-intercept equation as shown below:

$\begin{gathered} C=bM+k \\ b=35,k=70 \\ \\ \therefore\text{The equation is:} \\ C=35M+70 \end{gathered}$

B. The independent variable is the variable that we must know, in order to determine our dependent variable.

This means that the independent variable is the causative factor and the dependent variable is the result.

For this question, we need to enroll for a couple of months first, before we can determine the cost of our membership for that duration of time

Thus, the number of months (M) must be the independent variable, and the cost of the membership (C) must be the dependent variable.

C. We are asked to find the number of months of membership will $665.00 purchase at the club. Since we already know the causative relationship between the number of months (M) and the cost (C), we can use this formula to find the number of months (M).

This calculation is done below:

$\begin{gathered} C=35M+70 \\ \text{Given that, C= 665.00} \\ 665.00=35M+70 \\ \text{subtract 70 from both sides} \\ 665-70=35M \\ 595=35M \\ \text{Divide both sides by 35} \\ \frac{595}{35}=\frac{35M}{35} \\ \\ \therefore M=17 \end{gathered}$

Thus, the number of months of membership that $665.00 will purchase at the club is: 17 months

Final Answer

A. The linear equation in slope-intercept form is

$C=35M+70$

B. The number of months (M) must be the independent variable, and the cost of the membership (C) must be the dependent variable.

C. The number of months of membership that $665.00 will purchase at the club is: 17 months