Slope and Rate of Change

Slope and Rate of ChangeLesson 2.3

Warm-upDivide:

-10UndefinedAn Internet company had a profit of $2.6 million in retail sales over the last five years. What was its average annual profit?

Goal: Find and use the slope of a line.Slope of a nonvertical line is the ratio of the lines vertical change to its horizontal change.

Find the slope of the line that passes through the given pair of points:(-1, 5) and (3, 2)b. (-3, 2) and (5, -1)

c. (5, -2) and (5, 4)d. (.5, 4) and (7, 4)

Find the slope of the given line.

Classifying Lines by Slope

Positive slope m > 0Negative slope m < 0Zero slope m = 0Undefined slope m is undefinedLine rises fromLeft to RightLine falls fromLeft to RightLine is horizontalLine is verticalWithout graphing, tell whether the line through the given points rises, falls, is horizontal, or is vertical.1. (-3, -5) and (-5, -9)2. (-7, -8) and (-9, -8)

Rises

HorizontalHow can you describe how steep a line is?

m=2m=-2m=1m=-1m=1/4 m=-1/4 The slope of line tells you not only if the line rises, falls, is horizontal, or is vertical, but also how steep the line is. For two lines with positive slope, the line with the greater slope is steeper. For two lines with negative slope, the line whose slope has the greater absolute value is steeper.Which line is steeper?Line 1: through (-5, 4) and (2, 10) or Line 2: through (6, -2) and (-2, -8).Slope of Line 1: Slope of Line 2:

The slope of Line 1 is greater than the slope of Line 2 so Line 1 is steeperLine 1: through (21, 2) and (2, 27) or Line 2: through (2, 3) and (5, -5).Slope of Line 1: Slope of Line 2:

so Line 2 is steeperRate of Change In real-world situations, the slope of the line often represents an average rate of change, or how much a quantity changes, on average, compared to a given change in another quantity. A slope representing a rate of change will involve units of measure such as miles per hour or dollars per month.

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