3.5 equations of parallel & perpendicular lines with work
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3.5 Equations of Parallel & Perpendicular Lines with work
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Oct 2011:39 AM
3.5 Equations of Parallel & Perpendicular LinesWARMUP: ACT Practice The student body at Julian High School consists of sophomores, juniors, and seniors only. The ratio of sophomores to juniors to seniors on Julian High School's student council is 2:3:4. There are 15 juniors on the student council. How many students are on the entire student council?
F. 21
G. 24
H. 45
J. 60
K. 135
Oct 161:37 PM
Pull
Pull
3.5 Equations of Parallel & Perpendicular Lines with work
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Oct 1812:24 PM
Identifying SlopesTo find the slope of a line passing through two order pairs use the formula:
Match the 4 types of lines with the appropriate slopes: 1. Rising lines have a _________.
2. Falling lines have a _________.
3. Horizontal lines have a __________.
4. Vertical lines have a __________.
Positive Slope
Negative Slope
Slope of Zero
Undefined Slope
y2 y1 x2 x1 Rise
Run
Oct 1812:24 PM
Pairs of Lines• 1. Parallel Lines – same _______, different ___________
• 2. Coinciding Lines – same _______, same _________
• 3. Intersecting Lines – different ___________
Use these lines to show the above relationships on the graph to the right.
3.5 Equations of Parallel & Perpendicular Lines with work
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Nov 12:28 PM
Number yourselves 1 4 as a class.
Solve the problem that matches your number.
Get with the other people that have your same number and compare your work/answers.
Pick a person to be the group spokesperson and a person to be the recorder.
1 2
3 4
Oct 158:42 AM
MN and PQ for M(1,1), N(4,2), P(10,4) and Q(100,34)
Parallel, Perpendicular or Neither?
3.5 Equations of Parallel & Perpendicular Lines with work
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Oct 1812:24 PM
• Two nonvertical lines have the same _____ if and only if they are parallel.
Parallel Lines
Determine if the following quadrilateral with the given vertices is a parallelogram. Could it be a rectangle?
W(5,2); X(3,3); Y(3,5); Z(1,0)
Nov 137:48 AM
Equations Reading
Disagree or Agree
3.5 Equations of Parallel & Perpendicular Lines with work
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Oct 1812:24 PM
Perpendicular Lines• Two nonvertical lines are perpendicular if and only if the product of their slopes is ___.
• Perpendicular lines always form ___ degree angles.
• Example: What is the equation of a line perpendicular to TK with T( , ) and K( , ) going through point (3,4)?
0 2 5 0
Oct 149:49 AM
Write the equation of the line in slope intercept form going through points (4,6) and (2,5).
Writing Equations of Parallel & Perpendicular Lines
Now write the parallel line to the line above through the point (1, 1).
Now write the perpendicular line to the line above through the point (2, 3).
3.5 Equations of Parallel & Perpendicular Lines with work
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Oct 149:49 AM
Write the equation of the line in slope intercept form going through points (3,1) and (2,5).
Now write the parallel line to the line above through the point (1, 1).
Now write the perpendicular line to the line above through the point (2, 3).
Oct 1812:24 PM
Practice: Write an equation of the line that passes through the point (1, 5) and is
a) parallel to the line 3x + y = 5.
b) perpendicular to the line y = 3x 5.
3.5 Equations of Parallel & Perpendicular Lines with work
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Oct 2012:31 PM
Finding the Distance from a Point to a Line
Step 1: Write the line perpendicular
Step 2: Solve the system of equations using your perpendicular lines
Step 3: Use the distance formula to find the length from the coordinate given and the solution to the system.
Oct 2012:34 PM
Example: Find the distance from the point (6, 4) to the line y = x + 4.
Practice: Find the distance from the point (1, 6) to the line y = 2x.
3.5 Equations of Parallel & Perpendicular Lines with work
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Oct 2012:35 PM
HW: pg. 160:
A: 25, 29, 31, 33, 35, 37, 41, 43, 45, 52 57
B: 7, 11, 15, 19, 23, 25, 29, 31, 33, 35, 52 57
C: 7 31 odd, 52 57