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