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4.6 Slope

4.6 Slope. 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. Definition:

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4.6 Slope

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  1. 4.6 Slope 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.

  2. Definition: The slope m of a nonverticalline, 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)

  3. 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 please write Undefined as an answer! C (6, 12) D (6, 2)

  4. A Visual Interpretation of Slope Positive slope Zero slope Rising line Horizontal line Negative slope Undefined slope Falling line Vertical line

  5. Theorem 26:If two nonvertical lines are parallel, then their slopes are equal. Theorem 27: If the slopes of two nonvertical lines are equal, then the lines are parallel.

  6. 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 Theorem 28If two lines are perpendicular and neither is vertical, each line’s slope is the opposite reciprocal of the other’s. Theorem 29If a line’s slope is the opposite reciprocal of the another, the two lines are perpendicular.

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

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

  9. Homework: 4.6 Worksheet

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