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Section 3.1: Slope of a Line and Applications of Slope Worksheet 3.1



Slope: the steepness of a line.











Examples: Find the slopes of the lines pictured below.













Example: The graph gives the distance an automobile has traveled after different periods of time. Determine the slope of this line, and then interpret the meaning of this rate of change.



In general, the interpretation of slope is $\frac{\mbox{vertical units}}{\mbox{horizontal units}}$.











Formula for Slope: $m=\frac{y_2-y_1}{x_2-x_1}$.



Example: Calculate the slope of a line passing through the points $(-6, 2)$ and $(2, 9)$.













Fact 1: Slopes of parallel lines are equal.

Fact 2: Slopes of perpendicular lines are opposite reciprocals.















Example: Consider the line $L$ passing through the points $(-6, 2)$ and $(2, 9)$.

a. Calculate the slope of a line parallel to $L$.

b. Calculate the slope of a line perpendicular to $L$.









A Prehistoric Bird















Slopes of Horizontal and Vertical Lines