OBJECTIVES : STUDENTS WILL BE ABLE TO…

• IDENTIFY IF 2 L INES ARE PARALLEL , PERPENDICULAR OR NEITHER

•GRAPH A L INE PARALLEL OR PERPENDICULAR TO ANOTHER

•WRITE THE EQUATION OF A L INE THAT IS PARALLEL OR PERPENDICULAR TO A GIVEN LINE

Slopes of Parallel and Perpendicular Lines

What do you know about parallel lines??

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

Determining if 2 lines are parallel on the coordinate plane

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.

Step 1: find the slope of both lines using slope formula:

Step 2: Compare the slopes…are they the same? If yes, then the lines are parallel, if no, then they are not.

12

12

xx

yy

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 two lines parallel? Explain.

1. 2.

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

Compare Slopes by re-writing inslope-intercept form: y=mx+b Isolate y

Remember, “m” is the slope, not “mx”

Are the following lines parallel:

6x – 12y=8 and 2y = 4x -7

Graph a line parallel to the given line:

The following lines are perpendicular.

Calculate the slopes. What do you notice?

Slope and Perpendicular Lines

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

Ex) Slope: Perpendicular slope:2 -1/21/3 -3

The product of perpendicular slopes is -1

Any vertical and any horizontal line are perp.

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: Rewrite in slope int. form and compare slopes.

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

2. y=5x=-2

3. -3x+y=5 3x –y =4

Graph a line perpendicular to the given line.

Writing Equations of Parallel Lines

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

Step 1: Identify slope in given line

Step 2: Use the given slope ONLY and the given point ONLY to write the equation (y = mx +b)

Substitute m, x and y into y = mx + b

Solve for b:

Write equation using the m and the new b only:

EXAMPLE

Write the equation of a line parallel to y = ½ x +4 that passes through the point (-4, 3).

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 ONLY and given point ONLY to write new equation.

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

1. Identify slope of given line:

2. Write the perpendicular slope (this is what you use for the rest of the problem):

3. Use the slope from step 2 and the x and y given to write equation:

Example:

Write the equation of the line perpendicular to the line y=4x +1 that passes through the point (4, -5).

Another Form of a Line (EASY EASY!!)

POINT SLOPE FORM: y - y1 = m(x - x1)

m = slope(x1, y1) is a point on the line

Use if you know the slope of a line and one point.

Let’s write these equations in point-slope form…

1. Write the equation of a line parallel to y = ½ x +4 that passes through the point (-4, 3).

Identify slope of given line:

Use point give and slope to write line:

2. Write the equation of the line perpendicular to the line y=4x +1 that passes through the point (4, -5).

Identify slope of given line:

Write perpendicular slope:

Use perp. Slope and point to write equation: