Linear equation help

Question

Ana decides to start a tutoring company. She finds a place to rent for $400 dollars each month. Her tutoring costs $25 dollars per hour. Write a linear equation to model the problem. What are the independent and dependent variables in the problem? What’s the domain and range? What’s the x and y intercepts?

Answer 1

BACKGROUND INFORMATION:

A linear equation may be modeled by the equation y=mx+b where y is the dependent variable, m is the rate of change (slope), x is the independent variable, and b is the y-intercept (starting point of the dependent variable).

Use the acronym DRY MIX to remember that the dependent variable is also called the responding variable and is always modeled on the y-axis. The independent variable is also called the manipulated variable and is modeled on the x-axis.

ANSWER:

In this problem, Ana's independent variable x is the number of hours she tutors. Her dependent variable y is the amount of money she makes in dollars per month. Her y-intercept is -400 because this is the amount of fixed cost she incurs each month. For example, if she tutors for 0 hours, she will make -$400.

Thus, the linear equation to model this problem is:

y=25x-400

Domain: [0, infinity)

Range: [-400, infinity)

The x-intercept is Ana's breakeven point and can be calculated by setting the equation equal to 0.

0=25x-400

Add 400 to both sides

400=25x

Divide each side by 25

x=16

The x-intercept is 16 hours. Once Ana has tutored for 16 hours, she has "broke even" and made 0 dollars. Each additional hour of tutoring after 16 hours will result in profit.

The Domain describes the possible X values of this function. It is possible for Ana to tutor 0 or more hours per month and therefore the domain may be modeled as x is greater than or equal to 0, or [0, infinity)

The Range describes the possible Y values of this function. It is possible for Ana to make -$400 or more per month and therefore the range may be modeled as y is greater than or equal to -400, or [-400, infinity)

Answer 2

Business/expenses+25*teachers+400+profit