3.5 Equations of Parallel & Perpendicular Lines with answers

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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

3.5 Equations of Parallel & Perpendicular Lines with answers

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Pull

Pull

3.5 Equations of Parallel & Perpendicular Lines with answers

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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

RiseRun

Hint: Move box to the right

3.5 Equations of Parallel & Perpendicular Lines with answers

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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 answers

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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 answers

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• 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)

3.5 Equations of Parallel & Perpendicular Lines with answers

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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

3.5 Equations of Parallel & Perpendicular Lines with answers

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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 answers

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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).

3.5 Equations of Parallel & Perpendicular Lines with answers

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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 answers

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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.

3.5 Equations of Parallel & Perpendicular Lines with answers

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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 answers

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HW: pg. 160: 7, 9, 13, 17, 21, 25, 52 ­ 57