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Slope of A Line

Make a Prediction:. What is the value of the slope of the line?. Slope. Slope of A Line. Amount of Gas Used (gallons). Distance Traveled (miles). Attend to Meaning:. What does the slope represent in this case?.

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Slope of A Line

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  1. Make a Prediction: What is the value of the slope of the line? Slope Slope of A Line Amount of Gas Used (gallons) Distance Traveled (miles)

  2. Attend to Meaning: What does the slope represent in this case? 0.05 gallons per mile refers to the gas consumption efficiency of the particular vehicle Slope Slope of A Line Amount of Gas Used (gallons) Distance Traveled (miles)

  3. Attend to Meaning: What do the numerator “2” and the denominator “40” represent? Slope Slope of A Line Amount of Gas Used (gallons) Distance Traveled (miles)

  4. Attend to Meaning: What do the numerator “2” and the denominator “40” represent? Slope Slope of A Line Amount of Gas Used (gallons) 2 3 40 1 60 20 Distance Traveled (miles)

  5. Attend to Meaning: In general, what does slope mean? Change in values (dependent variable) Slope Change in values (independent variable) Rate of Change of dependent variable with respect to independent variable Slope of A Line Amount of Gas Used (gallons) 2 3 40 1 60 20 Distance Traveled (miles)

  6. True /False Question: Slope is essentially a “ratio as a measure”. Change in values (dependent variable) Slope Change in values (independent variable) Rate of Change of dependent variable with respect to independent variable Slope of A Line Amount of Gas Used (gallons) 2 3 40 1 60 20 Distance Traveled (miles)

  7. True /False Question: Slope is a rate—invariant ratio. Change in values (dependent variable) Slope Change in values (independent variable) Rate of Change of dependent variable with respect to independent variable Slope of A Line Amount of Gas Used (gallons) Distance Traveled (miles)

  8. Make a Prediction: If we let the horizontal axis represents the amount of gas and the vertical axis represents the distance, what is the value of the slope of the new line? Slope = ? Slope of A Line Distance Traveled (miles) Amount of Gas Used (gallons)

  9. Make a Prediction: If we let the horizontal axis represents the amount of gas and the vertical axis represents the distance, what is the value of the slope of the new line? Slope Slope of A Line Distance Traveled (miles) Amount of Gas Used (gallons)

  10. Question: How are the slopes of these two lines related? Distance Traveled (miles) Slope of A Line Amount of Gas Used (gallons) Amount of Gas Used (gallons) Distance Traveled (miles)

  11. Question: How are the slopes of these two lines related? Distance Traveled (miles) Slope of A Line Amount of Gas Used (gallons) Slopeg-d = 0.05 Sloped-g = 20 One slope is the reciprocal of the other: Amount of Gas Used (gallons) Distance Traveled (miles)

  12. Make a prediction: What is the value of the product of the 2 slopes? Distance Traveled (miles) Slope of A Line Amount of Gas Used (gallons) Amount of Gas Used (gallons) Distance Traveled (miles)

  13. Make a prediction: What is the value of the product of the 2 slopes? Distance Traveled (miles) Slope of A Line Amount of Gas Used (gallons) Amount of Gas Used (gallons) Distance Traveled (miles)

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