3-6:Slope of Parallel and Perpendicular Lines

Objective: To relate slope of parallel and perpendicular lines, and to write equations of parallel and perpendicular lines.

(http://www.regentsprep.org/Regents/math/ALGEBRA/AC3/Lparallel.htm)

Slopes of Parallel Lines

• Slopes of parallel lines are equal• Any 2 vertical lines are parallel; Any 2 horizontal lines

are parallel• Test whether 2 non-vertical or non-horizontal lines are

|| by comparing slopes

EXAMPLE: l1 contains points A(1,5) and B(3,1).

l2 contains points C(3,3) and D(1, -4)

Are the 2 lines parallel? Explain.

Are the two lines parallel?

Line 1 contains P(0,3) and Q(-2, 5)Line 2 contains R(0,-7) and S(3,-10)

Are the lines 4y-12x=20 and y=3x-1 parallel? Explain.

Compare Slopes by re-writing inslope-intercept form:

Slope and Perpendicular Lines

• Perpendicular Lines have slopes that are opposite, reciprocals of each other

• Their slopes’ product is -1• Any vertical and any horizontal line are perp.

Slope: Perpendicular Slope:

Are the 2 lines perpendicular? To answer this question, do the following:

1. Find their slopes2. If their slopes are opposite, reciprocal, then

they are perpendicular. Example:

line 1: (-2,3) and (6, -3)line 2: (-3,-2) and (0,2)

Are the 2 lines perpendicular:

1. 2x-y=5 y= -1/2x +7

2. y=5x=-2

3. -3x+y=5 3x –y =4

Writing Equations of Parallel Lines

Write an equation of a line parallel to y=-2x +3 that contains the point (1, -2).

Identify slope. Use this slope and given point to write equation:

Writing equations for perpendicular lines.

1. Identify slope of given line.2. Find the slope of the line perpendicular to

the given line (opposite, reciprocal)3. Use the slope from step 2 and given point to

write new equation.

Write the equation for the line perpendicular to y=-3x-5 that contains the point (-3, 7).

What do you see when you see an empty parrot cage?

A polygon.

HAHAHAHAHAHAHA………………………..