Lesson 4.2.  Determine the rate of change and slope of a line.

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Presentation transcript:

Lesson 4.2

 Determine the rate of change and slope of a line.

 A comparison of two measurements in which one of the terms has a value of 1.

 The ratio of the change in the output value and change in the input value of a function is called as Rate of Change.

DataRate of Change  Eve keeps a record of the number of lawns she mowed and the money earned.  Lawns$  115  345  690  8120  Constant  45 – 15  3 – 115  90 – 45  6 – 315  120 – 90  8 – 615

DataRate of Change  Height of football after it is kicked.  TimeHeight  00    226  Variable  18 – 0  0.5 – 036  31 – 18  1.5 – 513  26 – 31  2 – 1.526

DataRate of Change  The distance Nathan bicycled over time.  HoursMiles  115  230  345  460  Constant  30 – 15  2 – 115  45 – 30  3 – 215  60 – 45  4 – 315

 Given two points, find the slope.  (-3,2), (-6,4)  4 – 2  -6 – (-3)  2  -3  Slope = -2/3

 (4,3), (8,6)  6 – 3  8 – 4  3/4

 The graph shows the rate at which water is leaking from a tank. The slope of the line gives the leaking rate in gallons per minute.  Rise =3  Run =4  Rate= 3/4

 Characteristics of a graph that is proportional:  1) It passes through the origin.  2) It is a straight line.

12

PositiveNegative

No SlopeUndefined Slope

 (0, -1), (3,1)  2/3