Lesson #2: The Rate of Change

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Presentation transcript:

Lesson #2: The Rate of Change May 12, 2011

A rate of change tells us how a graph changes A rate of change tells us how a graph changes. If it changes slowly, steadily or quickly. The rate of change describes the SLOPE of a line or curve. Its units of measurement are determined by the units of measurement of the attributes that are being compared or examined. SLOPE (m)= rate of change m= change in y change in x

Numerically, rates of change are calculated by examining the “first differences”. These are the differences between consecutive dependent variable (y- variable) values. If the first differences are constant (all the same) we know that the graph is LINEAR. If the first differences are zero, this tells us that the line is flat along the horizontal.

If the first differences are not constant, we can use them to determine how the graph is changing, but to find the degree of the system we would have to find the second, or third differences.

EX1: use the first differences to comment on the rate of change and the trend of the graph. Hours 2 4 6 8 10 12 14 16 Earnings ($) 22 28 38 50 64 Analysis: