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Interpret Linear Functions: Mini-Lesson Review

Interpret Linear Functions: Mini-Lesson Review

Interpret Linear Functions: Mini-Lesson Review

Mini Lesson Question

Question #2: Interpret Linear Functions

When Quinn returned from vacation, he turned the heat back on in his home. He set the temperature as high as it could go. The function Q = 16 + 0.4 t represents the temperature in Quinn’s home (in degrees Celsius) after t minutes. 

How much will the temperature increase after 5 minutes?

  1. 0.4 degrees Celsius
  2. 20 degrees Celsius
  3. 18 degrees Celsius
  4. 2 degrees Celsius

Interpret Linear Functions

A linear function is a function that represents a line on the coordinate plane. A line can be written in slope-intercept form, y = m x + b y = m x + b , where m m is the slope and b b is the y y -intercept. The dependent variable is y y , and the independent variable is x x . The y y  can be replaced by f ( x ) f ( x ) , so the function can be written as f ( x ) = m x + b f ( x ) = m x + b .

Andrei wants to fill a glass tank with marbles, each with the same volume, and then fill the remaining space with water. The function V ( n ) = 32 − 0.05 n V ( n ) = 32 − 0.05 n represents the volume of water, in liters, Andrei uses if he uses n n marbles.

You can rewrite the function in slope-intercept form: V ( n ) = − 0.05 n + 32 V ( n ) = − 0.05 n + 32 . The slope is –0.05, and the y y -intercept is 32.

  1. What is the volume of the tank?

    V ( n ) = − 0.05 n + 32 V ( n ) = − 0.05 n + 32 represents the volume left in the tank after n n marbles were added. The volume of the tank is the initial volume before any of the marbles have been added, or V ( 0 ) V ( 0 ) . V ( 0 ) = − 0.05 ( 0 ) + 32 = 32 V ( 0 ) = − 0.05 ( 0 ) + 32 = 32 . The volume of the tank is 32 liters.

  2. What is the volume of each marble?

    The volume of water needed to fill the tank decreases by 0.05 liters each time Andrei puts in a marble, n n . This means that the volume of each marble is 0.05 liters.

Try it

Interpret Linear Functions

Rachel is a stunt driver, and she is escaping from a building that is about to explode. The function D ( t ) = − 38 t + 220 D ( t ) = − 38 t + 220 represents the remaining distance, D D , in meters after t t  seconds.

How long is the distance Rachel has to drive?

Here is how to interpret linear functions:

The function D ( t ) = − 38 t + 220 D ( t ) = − 38 t + 220 represents the remaining distance, D D , in meters after t t  seconds. The total distance she must travel is the initial value, or D ( 0 ) D ( 0 ) . D ( 0 ) = − 38 ( 0 ) + 220 = 220 D ( 0 ) = − 38 ( 0 ) + 220 = 220 . The total distance she must travel is 220 meters.

Check Your Understanding

The amount of money that farmers in Massachusetts paid to maintain their crops between 1991 and 2008 is modeled by the function P = 3.53 t + 100 P = 3.53 t + 100 , where P P  is the amount of money the farmers paid, in millions of dollars, and t t  is the year (with 1991 as t = 0 t = 0 ). What does the 3.53 mean in the equation?

  1. The costs for maintaining crops increased by $3.53 million each year between 1991 and 2008.

  2. The costs for maintaining crops increased a total of $3.53 million between 1991 and 2008.

  3. The costs for maintaining crops was $3.53 million in 1991.

  4. The costs for maintaining crops was $3.53 million in 2008.

The costs for maintaining crops increased by $3.53 million each year between 1991 and 2008.

Check yourself: 3.53 is the rate of increase each year, or slope. It represents the ratio of the amount of money the farmers paid (cost) over the amount of time they paid (per year).

Videos: Interpreting Linear Functions

Khan Academy: Interpret Linear Functions

Watch the videos to see how to interpret a linear function.

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