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Math 110 (Lehmann) 1.3 & 1.4 Lecture Slides

Math 110 (Lehmann) 1.3 & 1.4 Lecture Slides . Exact Linear Relationships & Approximate Linear Relationships. x and y -intercepts. An x -intercept is any point where the graph touches the x-axis. It is a point ( __ , 0)

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Math 110 (Lehmann) 1.3 & 1.4 Lecture Slides

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  1. Math 110 (Lehmann)1.3 & 1.4 Lecture Slides Exact Linear Relationships & Approximate Linear Relationships

  2. x and y-intercepts An x-intercept is any point where the graph touches the x-axis. It is a point ( __ , 0) The y-intercept is the point where the graph touches the y-axis. It is a point (0, __ ) What is the x-intercept of this graph? What is the y-intercept?

  3. Altitude of a Balloon after t-minutes

  4. Independent Variable: t = time in minutes Dependent Variable: A = altitude in feet Since we could connect all of the data points with a line, this data is exactly linear.

  5. Since we could connect all of the data points with a line, this data is exactly linear. • The line that we draw is called a linear model, and we can use it to make estimates. • What altitude do you think the balloon was at after 3 minutes? • When do you think the balloon will reach an altitude of 1500 feet? • When do you think the balloon will hit the ground?

  6. What are the coordinates of theA-intercept? What is the meaning of this point in this problem? What are the coordinates of thet-intercept? What is the meaning of this point in this problem?

  7. Sometimes data is not exactly linear, but it is still approximately linear. For reference: 0 decibels = faintest sound humans can hear 20 decibels = whisper 60 decibels = normal conversation 80 decibels = noisy street corner 100 decibels = soft rock concert 120 decibels = threshold of pain

  8. Does this data appear to be exactly linear, approximately linear,or just some random a$$ %*!# ?

  9. This data is notexactly linear, but it is approximately linear. So we can still • Use a line to model the data. • How should we set the volume knob to put out 80 decibels? • What is the y-intercept? What is its meaning? • What would you guess the x-intercept is? What is its meaning? • What do you call it when a model does not make sense past a certain point?

  10. Problem #1: Cash for Clunkers Make a scattergram for the following data and then draw a linear model that fits the data. Use your linear model to answer the questions. (a.) Is the data exactly linear or approximately linear? (b.) How much did the car cost when it was new? (c.) When does model breakdown occur?

  11. Value of a car after t-years

  12. Problem #2: Dude, Where’s My Phone? Make a scattergram for the following data and then draw a linear model that fits the data. Use your linear model to answer the questions. (a.) Is the data exactly linear or approximately linear? (b.) According to your model, when will there be ½ million pay phones? (c.) What is the P-intercept? What is its meaning? (d.) What is the t-intercept? What is its meaning? (e.) According to the model, how many pay phones will there be in 2015?

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