parallel and perpendicular slopes lines
TRANSCRIPT
Slope, Parallel and Perpendicular Lines
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Try these…..Review
1.Find the reciprocal of each fraction
a. b. c. d.
2.Find the slope and y-intercept of each equation
21
34
31
25
26 d.6 c.835b.4
45 a. xyxyxyxy
Quick Review/Preview
1. What is the Slope-Intercept Form? y = mx + b
2. What is the Standard Form? Ax + By = C
3. What is the Point-Slope Form?y – y1 = m(x – x1)
4. Find the “negative reciprocal” of each fraction
34d.
21c.
73b.
52a.
432
12
37
25
Overview
How to calculate a slope Parallel Lines and Perpendicular Lines Write equations for each type of lines
NotesFinding the Slope of a Line
Slope is found using the equation m= y2 -y1.
x2 -x1
The coordinates for the points on the graph are plugged into the equation above. The equation is then solved and the remaining solution is the slope. Example:Let (x1, y1) = (-3, 5) and (x2, y2) = (2, 1)
NotesClassifying Lines Using Slope A line with a positive slope rises from left to right. (m>0) A line with a negative slope falls from left to right. (m<0) A line with a slope of zero is horizontal. (m=0) A line with an undefined slope is vertical. (m is undefined.)
Positive Slope Negative Slope Zero Slope Undefined Slope
Notes ContinuedSlopes of Parallel and Perpendicular LinesParallel Lines The lines are parallel if and only if they have the same
slope. m1 = m2
Perpendicular Lines The lines are perpendicular if and only if their slopes are negative reciprocals of each other
m1 = - 1 or m1m2 = -1 m2
Parallel Lines Perpendicular Lines
Parallel Lines
Parallel Lines - lines that never intersect
What is the slope of thered line?
1/2What is the slope of theblue line?
1/2Parallel Lines have the slope!same
Parallel Lines
Determine if the lines are parallel
1. 2x + 6y = 12 6y = -2x + 12
yes
531 and1262 xyyx
231
xy
Parallel Lines
Determine if the lines are parallel
2. 6x + 8y = -248y = -6x – 24
No
343 and 2486 xyyx
343
xy
Parallel Lines
Determine if the lines are parallel
3.4x + 6y = -26y = -4x – 2
No
832 and 264 xyyx
31
32
xy
Perpendicular Lines
Perpendicular Lines – lines that intersect to form right angles
What is the slope of thered line?
-1/4What is the slope of theblue line?
4/1Perpendicular Lines have slope!negative reciprocal
Perpendicular Lines
What is the slope of the perpendicular line?
7. -5/2
8.5/1 = 5
9.1/2
852
xy
xy51
72 xy
Equations of Perpendicular Lines
10. Find the equation of the line that contains (0, -2) and is perpendicular to y = 5x + 3
m = 51
xy512
Equations of Perpendicular Lines
11. Find the equation of the line that contains (1, 8) and is perpendicular to
m =
143
xy
34
1348 xy
Equations of Perpendicular Lines
12. Find the equation of the line that contains (2, -3) and is perpendicular to
m = 2
y + 3 = 2(x – 2)
621
xy
Perpendicular Lines13. Determine if the lines are perpendicular:
and
No14. Determine if the lines are perpendicular:
and
Yes
423132
xyxy
934534
xyxy
423 xy423 xy
34
32
xy
934 xy934 xy
49
43
xy
Challenge
What is the slope of the line that is parallel to x = 4?
undefined What is the slope of the line that is
perpendicular to x = 4?zero