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Independent and Independent and Dependent QuantitiesDependent Quantities

Key PointsKey Points Independent and Dependent Quantities Independent and Dependent Quantities

must be variablesmust be variables (letters), not (letters), not constants (numbers- including constants (numbers- including ππ).).

Independent-Independent- often quantities that often quantities that cannot be controlled like cannot be controlled like time time andand weatherweather

Dependent-Dependent- change as a result of the change as a result of the Independent Quantities like Independent Quantities like distance distance and and total costtotal cost

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Independent and Independent and DependentDependent

In an equation, In an equation, xx (input) (input) represents the represents the independentindependent quantity and quantity and yy (output) (output) represents the represents the dependentdependent quantityquantity

Ex: Ex: yy = 2 = 2xx + 3 + 3

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Dependent Independent

Independent and Independent and DependentDependent

Sometimes equations have other Sometimes equations have other variables, not x and y.variables, not x and y.

Ex. Ex. d d = 54= 54tt

Dependent Independent

The variable by itself is always dependent!

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Independent and Independent and Dependent Quantities, Dependent Quantities,

continued…continued… When no equation is given:When no equation is given:

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A car salesman made a chart showing the relationship between the number of cars he sells and the months of the year.

Now ask yourself, does the number of cars depend on the months of the year

or do the months of the year depend on the number of cars?

Because the number of cars will change based on the month, the number of cars is dependent, and the month is independent.

A fur coat salesman made a table showing the relationship between the average daily temperature and the number of coats he sells per day. Identify the independent and dependent variables in this situation.

Independent _________________________

Dependent __________________________

To find c, the total cost of an order of DVDs from To find c, the total cost of an order of DVDs from a certain website, the equation c=19.99n + 4.99 a certain website, the equation c=19.99n + 4.99 can be used, where n represents the number of can be used, where n represents the number of DVDs ordered. If c is a function of n, which of DVDs ordered. If c is a function of n, which of the following best describes this relationship?the following best describes this relationship?

A. The value of n is constant in relation to cB. The value of n is dependent on cC. The value of c is constant in relation to nD. The value of c is dependent on n

For a jogger traveling at a speed of 6 miles per hour, the relationship between the distance traveled, d, and the time traveled, t, is described by the function d = 6t. Which statement is true?

A. The time traveled depends on the distance traveledB. The distance traveled depends on the time traveledC. The speed of the runner depends on the distance traveledD. The speed of the runner depends on the time traveled

The cost, c, of purchasing r roses, can be found by using the equation c = 3.75 + 2.15r, where r represents the number of roses purchased. Which of the following best represents this situation?

A. The value of r is constant in relation to cB. The value of c is constant in relation to rC. The value of c is dependent on rD. The value of r is dependent on c

A city water employee is making a table showing the relationship between the average daily temperature and the city’s water usage. What is the independent quantity?

Tessa wants to determine the relationship between the number of absences a student has and their grade point average. What is the dependent variable in this situation?