# graphing parallel and perpendicular lines. review slope intercept form y = mx + b m = slope m =...

Embed Size (px)

TRANSCRIPT

Graphing Parallel and Graphing Parallel and Perpendicular LinesPerpendicular Lines

ReviewReview

Slope intercept formSlope intercept form

y = y = mmx + x + bb mm = slope= slope b = y-interceptb = y-intercept

Slope FormulaSlope Formula

Parallel LinesParallel Lines

If two nonvertical lines in the same plane If two nonvertical lines in the same plane have the same slope, they are parallel.have the same slope, they are parallel.

Parallel linesParallel linesSame slopeSame slopeDifferent y-interceptsDifferent y-intercepts

Examples of Parallel linesExamples of Parallel lines

http://www.flickr.com/photos/annfrau/galleries/72157622379459686/

http://fakeexpressionsoftheunkown.wordpress.com/2008/04/14/photo-parallel-lines/

ExampleExample

Line 1: Line 1: y = 2x + 1y = 2x + 1 Line 2: Line 2: y = 2x - 3y = 2x - 3

These two lines are parallel because they have the same slope. No matter how far they continue on, they will NEVER cross each other!

Are these equations parallel?Are these equations parallel?

15

3 xy

2

1

3

4 xy 1

3

4 xy

75

3 xy1.

2.

3.

63 xy 13

1 xy

How do you write the equation How do you write the equation for a parallel line with only a for a parallel line with only a

point and a slope?point and a slope?

Use these steps….Use these steps….Write an equation of the line that passes through the Write an equation of the line that passes through the

point (-3, -5) and is parallel to the line y = 3x - 1point (-3, -5) and is parallel to the line y = 3x - 1

- Step 1: what is the slopeslope? m = 3m = 3

- Step 2: To find the new y-intercept- Step 2: To find the new y-intercept

Plug the slope and given point into y = Plug the slope and given point into y = mmx + x + bb

-5 = 3(-3) + b

-5 = -9 + b4 = bb

- Step 3: Write an equation. Use y = mx + b.

y = 3x + 4

Other examplesOther examplesWrite an equation of the line that passes through the Write an equation of the line that passes through the

point (-2,11) and is parallel to the line y = -x + 6. point (-2,11) and is parallel to the line y = -x + 6. Then graph the lines to see if they’re parallel.Then graph the lines to see if they’re parallel.

m = -1 Parallel lineParallel line – y = -x + 9

Write an equation of the line that passes through the point (-2,5) and is parallel to the line 2y = 4x - 6. Then graph the lines to see if they’re parallel.

m = 2 Parallel lineParallel line – y = 2x + 9

Perpendicular LinesPerpendicular Lines If two nonvertical lines in the same plane have If two nonvertical lines in the same plane have

slopes that are negative reciprocals, then the slopes that are negative reciprocals, then the lines are perpendicular. lines are perpendicular.

Perpendicular linesPerpendicular linesSlopes are negative reciprocals of each otherSlopes are negative reciprocals of each otherWhen lines intersect they form a right angleWhen lines intersect they form a right angle i.e. Horizontal and vertical lines are perpendicular i.e. Horizontal and vertical lines are perpendicular

to each otherto each other

Examples of perpendicularExamples of perpendicular

http://futureofmath.misterteacher.com/digitalcameras.html

http://www.valdosta.edu/~amcrosby/ebook5.html

http://www.valdosta.edu/~amcrosby/ebook4.html

Are these equations perpendicular?Are these equations perpendicular?

52 xy 132 xy

43

1 xy1. 53 xy

4

1

2

3 xy 12

3

2 xy

2.

3. 6xy 2 xy

4.

Determine whether these line are Determine whether these line are parallel or perpendicular.parallel or perpendicular.

Line a: y = 5x – 3Line a: y = 5x – 3 Line b: x + 5y = 2 Line b: x + 5y = 2

Line c: -10y – 2x = 9Line c: -10y – 2x = 9

5

2

5

1 xy

Step 1: Put each equation into slope-intercept form

Line a: y = 5x - 3 Line b: Line b:

Line c: xy5

1

Parallel

Line b & Line c

Perpendicular

Line a & Line b; Line a & Line c

Which are parallel? Which are perpendicular?

ExampleExampleWrite an equation of the line that passes through Write an equation of the line that passes through

(4,-5) and is perpendicular to the line (4,-5) and is perpendicular to the line

y = 2x + 3.y = 2x + 3.- Step 1: what is the slopeslope? m = 2m = 2

Because the slopes of perpendicular lines are negative reciprocals, so your new slope must be -½.

Plug the new slope and given point into y = Plug the new slope and given point into y = mmx + x + bb

-5 = -½(4) + b

-5 = -2 + b -3 = bb

- Step 3: Write an equation. Use y = mx + b.

y = -½x - 3

Other examplesOther examplesIs Is Line aLine a perpendicular to perpendicular to Line bLine b??

Line a: 2y + x = -12Line a: 2y + x = -12 Line b: 2y = 3x - 9

Write an equation of the line that passes through (4,3) and is perpendicular to the line y = 4x – 7.

HomeworkHomework

For homework, you will be completing For homework, you will be completing WS 4DWS 4D..

We will go over any questions on it tomorrow We will go over any questions on it tomorrow before you turn it in.before you turn it in.