Objective: After studying this lesson you will be able to understand the concept of slope, relate the slope of a line to its orientation in the coordinate.

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Presentation transcript:

Objective: After studying this lesson you will be able to understand the concept of slope, relate the slope of a line to its orientation in the coordinate plane and recognize the relationships between slopes of parallel and perpendicular lines.

DefinitionThe slope m of a nonvertical line, segment, or ray containing (x1, y1) and (x2, y2) is defined by the formula Example. Find the slope of the segment joining (-2, 3) and (6, 5)

When the slope formula is applied to a vertical line such as line CD, the denominator is zero. Division by zero is undefined, so a vertical line has no slope. D (6, 2) C (6, 12)

A Visual Interpretation of Slope No slope Vertical line Zero slope Horizontal line Negative slope Falling line Positive slope Rising line

TheoremIf two nonvertical lines are parallel, then their slopes are equal. TheoremIf the slopes of two nonvertical lines are equal, then the lines are parallel.

It can also be shown that there is a relationship between the slopes of two perpendicular lines— they are opposite reciprocals of each other. example TheoremIf two lines are perpendicular and neither is vertical, each line’s slope is the opposite reciprocal of the other’s. TheoremIf a line’s slope is the opposite reciprocal of the another, the two lines are perpendicular.

1. If A = (4, -6) and B = (-2, -8), find the slope of line AB. 2. Show that CEF is a right triangle You Try! F (4, 7) E (8, 4) C (1, 3)

3.Given: ABE as shown Find: a. The slope of the altitude AC b. The slope of the median AD A (-2, 10) E (6, 5) B (-4, 3)

Summary: Homework: worksheet Describe how to find slope. How can you tell without graphing if lines are parallel? Perpendicular?