Concept explainers
(a)
To find:The equation that represents the cost C of a membership for m months.
(a)
Answer to Problem 59PPS
The equation that represents the cost C of a membership for mmonthsis
Explanation of Solution
Given:
The startup fee for the gym
The monthly fee for the gym =
Calculation:
The standard form of slope and intercept form of the straight line is
Here m is the slope of the straight line and c is the y- intercept of the equation.
The startup fee is the intercept of the line on the y- axis while the monthly fee is the slope of the equation.
Write the equation for the given situation.
Substitute
The equation of the straight line in the slope and intercept form is
Here, m is the number of months.
Therefore, the equation of the straight line is
(b)
To find:The meaning of slope in equation.
(b)
Answer to Problem 59PPS
The slope in the equation represents the rate of fee variation per month.
Explanation of Solution
Given:
The startup fee for the gym
The monthly fee for the gym =
Calculation:
The standard form of slope and intercept form of the straight line is
Here m is the slope of the straight line and c is the y- intercept of the equation.
The startup fee is the intercept of the line on the y- axis while the monthly fee is the slope of the equation.
Write the equation for the given situation.
Substitute
The equation of the straight line in the slope and intercept form is
Here, m represents number of months. The slope of the equation is 45 which represents the rate of fee variation.
Therefore, the equation of the straight line is
(c)
To find:The meaning of C intercept in equation.
(c)
Answer to Problem 59PPS
The intercept in the equation represents the constant one time fee.
Explanation of Solution
Given:
The startup fee for the gym
The monthly fee for the gym =
Calculation:
The standard form of slope and intercept form of the straight line is
Here m is the slope of the straight line and c is the y- intercept of the equation.
The startup fee is the intercept of the line on the y- axis while the monthly fee is the slope of the equation.
Write the equation for the given situation.
Substitute
The equation of the straight line in the slope and intercept form is
Here, m represents number of months. The intercept of the equation is 145 which represents the startup fee to be submitted once. This startup fee is independent of variations over time.
Therefore, the equation of the straight line is
(d)
To find:The cost of a two year membership.
(d)
Answer to Problem 59PPS
The cost of two year membership is
Explanation of Solution
Given:
The startup fee for the gym
The monthly fee for the gym =
Calculation:
The standard form of slope and intercept form of the straight line is
Here m is the slope of the straight line and c is the y- intercept of the equation.
The startup fee is the intercept of the line on the y- axis while the monthly fee is the slope of the equation.
Write the equation for the given situation.
Substitute
The equation of the straight line in the slope and intercept form is
Here, m represents number of months. Substitute 24 months for m in the equation for 2 years.
Therefore, the cost for two year membership is
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