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Slope of A Line Distance Traveled (miles) Make a Prediction: What is the value of the slope of the l Slope 1 2 1 2 x x y y 20 60 1 3 40 2 05 . 0
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Slope of A Line
Distance Traveled (miles)
Make a Prediction: What is the value of the slope of the line?
Slope 12
12
xx
yy
2060
13
40
2
05.0
Slope of A Line
Distance Traveled (miles)
Attend to Meaning: What does the slope represent in this case?
Slope 12
12
xx
yy
2060
13
40
2
05.0
0.05 gallons per mile refers to the
gas consumption efficiency of the particular vehicle
Slope of A Line
Distance Traveled (miles)
Attend to Meaning: What do the numerator “2” and the denominator “40” represent?
Slope 12
12
xx
yy
2060
13
40
2
05.0
Slope of A Line
Distance Traveled (miles)
Attend to Meaning: What do the numerator “2” and the denominator “40” represent?
Slope 12
12
xx
yy
2060
13
40
2
05.060
20
3
1
2
40
Slope of A Line
Distance Traveled (miles)
Attend to Meaning: In general, what does slope mean?
Slope 12
12
xx
yy
2060
13
40
2
05.060
20
3
1
2
40
Change in values (dependent variable)
Change in values (independent variable)
Rate of Change of dependent variable with
respect to independent
variable
Slope of A LineTrue /False Question: Slope is essentially a “ratio as a measure”.
Distance Traveled (miles)
Slope 12
12
xx
yy
2060
13
40
2
05.060
20
3
1
2
40
Change in values (dependent variable)
Change in values (independent variable)
Rate of Change of dependent variable with
respect to independent
variable
Slope of A LineTrue /False Question: Slope is a rate—invariant ratio.
Distance Traveled (miles)
Slope 12
12
xx
yy
2060
13
40
2
05.0
Change in values (dependent variable)
Change in values (independent variable)
Rate of Change of dependent variable with
respect to independent
variable
Slope of A LineMake 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?
Amount of Gas Used (gallons)
Slope = ?
Slope of A LineMake 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?
Amount of Gas Used (gallons)
Slope valueshorizontalin change
valueslin vertica change
34
6080
1
20
20
Slope of A LineQuestion: How are the slopes of these two lines related?
Amount of Gas Used (gallons)Distance Traveled (miles)
Slope of A LineQuestion: How are the slopes of these two lines related?
Sloped-g = 20
Amount of Gas Used (gallons)Distance Traveled (miles)
Slopeg-d = 0.05
One slope is the reciprocal of the other: d-g
g-d Slope
1Slope
Slope of A Line
Amount of Gas Used (gallons)Distance Traveled (miles)
?Slope Slope d-gg-d
Make a prediction: What is the value of the product of the 2 slopes?
Slope of A Line
Amount of Gas Used (gallons)Distance Traveled (miles)
1Slope Slope d-gg-d
Make a prediction: What is the value of the product of the 2 slopes?
