Outline Parallel and Perpendicular Lines Slope as Rate of Change
College Algebra & Trigonometry I 2.4 - More on Slope Math 1100
April 2, 2007
Math 1100
College Algebra & Trigonometry I
Outline Parallel and Perpendicular Lines Slope as Rate of Change
1
Parallel and Perpendicular Lines Parallel Lines Perpendicular Lines
2
Slope as Rate of Change Rate of Change Average Rate of Change
Math 1100
College Algebra & Trigonometry I
Outline Parallel and Perpendicular Lines Slope as Rate of Change
Parallel Lines Perpendicular Lines
Slope and Parallel Lines
If two nonvertical lines are parallel, they have the same slope.
Math 1100
College Algebra & Trigonometry I
Outline Parallel and Perpendicular Lines Slope as Rate of Change
Parallel Lines Perpendicular Lines
Slope and Parallel Lines
If two nonvertical lines are parallel, they have the same slope. If two distinct nonvertical lines have the same slope, they are parallel.
Math 1100
College Algebra & Trigonometry I
Outline Parallel and Perpendicular Lines Slope as Rate of Change
Parallel Lines Perpendicular Lines
Slope and Parallel Lines
If two nonvertical lines are parallel, they have the same slope. If two distinct nonvertical lines have the same slope, they are parallel. Two distinct vertical lines are parallel.
Math 1100
College Algebra & Trigonometry I
Outline Parallel and Perpendicular Lines Slope as Rate of Change
Parallel Lines Perpendicular Lines
Example Example Write an equation of the line passing through (-3, 1) and parallel to line whose equation is y = 2x + 1. Express the equation in point-slope form and slope-intercept form.
Math 1100
College Algebra & Trigonometry I
Outline Parallel and Perpendicular Lines Slope as Rate of Change
Parallel Lines Perpendicular Lines
Answer point-slope form: y − 1 = 2(x − (−3)) y − 1 = 2(x + 3)
Math 1100
since the slope m is 2
College Algebra & Trigonometry I
Outline Parallel and Perpendicular Lines Slope as Rate of Change
Parallel Lines Perpendicular Lines
Answer point-slope form: y − 1 = 2(x − (−3)) y − 1 = 2(x + 3)
since the slope m is 2
slope-intercept form: y − 1 = 2(x + 3) (point-slope form) y = 2x + 6 + 1 y = 2x + 7
Math 1100
College Algebra & Trigonometry I
Outline Parallel and Perpendicular Lines Slope as Rate of Change
Parallel Lines Perpendicular Lines
Slope and Perpendicular Lines
If two nonvertical lines are perpendicular, then the product of their slopes is -1..
Math 1100
College Algebra & Trigonometry I
Outline Parallel and Perpendicular Lines Slope as Rate of Change
Parallel Lines Perpendicular Lines
Slope and Perpendicular Lines
If two nonvertical lines are perpendicular, then the product of their slopes is -1.. If the product of two slopes is -1, then the lines are perpedicular.
Math 1100
College Algebra & Trigonometry I
Outline Parallel and Perpendicular Lines Slope as Rate of Change
Parallel Lines Perpendicular Lines
Slope and Perpendicular Lines
If two nonvertical lines are perpendicular, then the product of their slopes is -1.. If the product of two slopes is -1, then the lines are perpedicular. A horizontal line and a vertical line are perpendicular.
Math 1100
College Algebra & Trigonometry I
Outline Parallel and Perpendicular Lines Slope as Rate of Change
Parallel Lines Perpendicular Lines
Example Example Write the equation of the line passing through (2, −5) and perpendicular to the line whose equation is x + 5y − 9 = 0. Write the equation in general form.
Math 1100
College Algebra & Trigonometry I
Outline Parallel and Perpendicular Lines Slope as Rate of Change
Parallel Lines Perpendicular Lines
Answer The slope for equation x + 5y − 9 = 0 is −1/5
Math 1100
College Algebra & Trigonometry I
Outline Parallel and Perpendicular Lines Slope as Rate of Change
Parallel Lines Perpendicular Lines
Answer The slope for equation x + 5y − 9 = 0 is −1/5 So the slope of the perpendicular line has to be 5.
Math 1100
College Algebra & Trigonometry I
Outline Parallel and Perpendicular Lines Slope as Rate of Change
Parallel Lines Perpendicular Lines
Answer The slope for equation x + 5y − 9 = 0 is −1/5 So the slope of the perpendicular line has to be 5. point-slope form: y − (−5) = 5(x − 2) y + 5 = 5x − 10 y − 5x + 15 = 0
Math 1100
College Algebra & Trigonometry I
Outline Parallel and Perpendicular Lines Slope as Rate of Change
Rate of Change Average Rate of Change
Slope as Rate of Change: Example The line graph represents the number of men and women living alonge. Find the slope of the line segment for women and describe what this slope represents (see textbook page 234, Example 3).
Math 1100
College Algebra & Trigonometry I
Outline Parallel and Perpendicular Lines Slope as Rate of Change
Rate of Change Average Rate of Change
Slope and Average Rate of Change Definition Let (x1 , f (x1 )) and (x2 , f (x2 )) be two distinct points on the graph of a function f . The average rate of change of f from x1 to x2 is AVGRate =
Math 1100
f (x2 ) − f (x1 ) x2 − x1
College Algebra & Trigonometry I
Outline Parallel and Perpendicular Lines Slope as Rate of Change
Rate of Change Average Rate of Change
Example Example Find the average rate of change of f (x) = x 2 from x1 = 0 to x2 = 1 x1 = 0 to x2 = 2 x1 = −1 to x2 = 1
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Outline. Logarithm Functions. Logarithms Properties. College Algebra & Trigonometry I. 4.2 - Logarithm Functions. Math 1100. North Carolina Central University.
2.8 - Distance and Midpoint Formulas; and Circles. Math 1100. North Carolina Central University. Math & C.S. Department. Hicham Qasmi - [email protected].
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