Ch. 3 3.6 & 3.7 || and  lines HMWK: p. 168, #s 12 – 42 (x 3), 49 – 52 p. 175, #s 15 – 36 (x 3), 39 – 51 odd Game Plan: Today I will be able to  Calculate.

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Presentation transcript:

Ch & 3.7 || and  lines HMWK: p. 168, #s 12 – 42 (x 3), 49 – 52 p. 175, #s 15 – 36 (x 3), 39 – 51 odd Game Plan: Today I will be able to  Calculate the slope of || and  lines  Use slopes to determine || or  lines Warm-Up: 1.State whether the slope of the line is positive, negative, undefined, or zero. a.Rises from left to right b.Vertical c.Horizontal d.Falls from left to right 2.How do you find the slope of a line?

Ch & 3.7 || and  lines Review … 1.Given the following points, find the slope (0,6) and (5,2). 2.Using the information from #1, write the equation of the line in slope-intercept form. Slope m = -4/5 y = (-4/5)x + 6

Ch & 3.7 || and  lines Parallel Lines Postulate: In a coordinate plane, two nonvertical lines are parallel if and only if they have the same slope. Any two vertical lines are parallel. What does this actually mean? Parallel lines Have the same slope All vertical lines are parallel Don’t write this yet! This is the good stuff!

Ch & 3.7 || and  lines Example 1.Find the slope of each line. Is m 1 || m 2 ? 2. Line m 1 has the equation y = 3x-7. Line m 2 is parallel to m 1 and passes through the point (-2,1). Write an equation of m 2. m 1 = 7/3 & m 2 = 2 Not parallel y = 3x+7

Ch & 3.7 || and  lines Investigate & discover Materials: ruler, graph paper, and a group Task:  Work in groups of three  Complete activity number given to your group  Complete #5 also  Have 7minutes to complete

Ch & 3.7 || and  lines Perpendicular Lines Postulate: In a coordinate plane, two nonvertical lines are perpendicular if and only if the product of their slope is –1. Vertical and horizontal lines are perpendicular. Don’t write this yet!

Ch & 3.7 || and  lines Perpendicular Lines What does this actually mean? Perpendicular lines Product of slopes = -1 m 1 =3 and m 2 =(- 1 / 3 ) (m 1 )(m 2 ) = (3)(- 1 / 3 ) = -1 Slopes are negative reciprocals m 1 =3 and m 2 =(- 1 / 3 ) or m 1 =( a / b) and m 2 =(- b / a ) Vertical & horizontal are  This is the good stuff!

Ch & 3.7 || and  lines Examples 1.Line r goes through (-2,2) and (5,8). Line s goes through (-8,7) and (-2,0). Is r  s? 2. An equation for line v is An equation for line w is 8x + 3y = 10. Is v  w? 3.Line g has equation y = 3x-2. Find the equation of the line h that passes through (3,4) and is perpendicular to g. Yes No y = - 1 / 3 x+5

Ch & 3.7 || and  lines Wrap - Up If your friend was absent today, how would you explain the slope relationships with parallel and perpendicular lines?