ch. 3 3.6 & 3.7 || and lines hmwk: p. 168, #s 12 – 42 (x 3), 49 – 52 p. 175, #s 15 – 36...
TRANSCRIPT
Ch. 33.6 & 3.7 || and lines
HMWK:p. 168, #s 12 – 42 (x 3), 49 – 52p. 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 rightb. Verticalc. Horizontald. Falls from left to right
2. How do you find the slope of a line?
Ch. 33.6 & 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. 33.6 & 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 y
et!
This is the good stuff!
Ch. 33.6 & 3.7 || and lines
Example
1. Find the slope of each line.
Is m1 || m2?
2. Line m1 has the equation y = 3x-7. Line m2 is parallel to m1 and passes through the point (-2,1). Write an equation of m2.
m1 = 7/3 & m2 = 2
Not parallel
y = 3x+7
Ch. 33.6 & 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. 33.6 & 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. 33.6 & 3.7 || and lines
Perpendicular Lines
What does this actually mean?Perpendicular lines • Product of slopes = -1
m1=3 and m2=(-1/3)
(m1)(m2) = (3)(- 1/3) = -1
• Slopes are negative reciprocalsm1=3 and m2=(- 1/3) or
m1=(a/b) and m2=(- b/a)
• Vertical & horizontal are
This is the
good stuff!
Ch. 33.6 & 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.
.8
5
8
3 xy
Yes
No
y = -1/3x+5
Ch. 33.6 & 3.7 || and lines
Wrap - Up
If your friend was absent today, how would you explain the slope relationships with parallel and perpendicular lines?