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Slope of A Line

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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?

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)