4-7B Perpendicular Lines Algebra 1 Glencoe McGraw-HillLinda Stamper.
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Transcript of 4-7B Perpendicular Lines Algebra 1 Glencoe McGraw-HillLinda Stamper.
![Page 1: 4-7B Perpendicular Lines Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649d0a5503460f949dcd0d/html5/thumbnails/1.jpg)
4-7B Perpendicular Lines
Algebra 1 Glencoe McGraw-Hill Linda Stamper
![Page 2: 4-7B Perpendicular Lines Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649d0a5503460f949dcd0d/html5/thumbnails/2.jpg)
What is the reciprocal of 8?What is the opposite reciprocal of 8?
In this lesson you will need to find and use opposite reciprocals.
81
81
![Page 3: 4-7B Perpendicular Lines Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649d0a5503460f949dcd0d/html5/thumbnails/3.jpg)
Two lines in a coordinate plane are perpendicular if they intersect at right angles (90 degree angles).
Horizontal and vertical lines are perpendicular to each other.
x
y
![Page 4: 4-7B Perpendicular Lines Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649d0a5503460f949dcd0d/html5/thumbnails/4.jpg)
In a coordinate plane, two non vertical lines are perpendicular if and only if the product of their slopes is –1.
x
y
Do you think these lines are perpendicular?
![Page 5: 4-7B Perpendicular Lines Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649d0a5503460f949dcd0d/html5/thumbnails/5.jpg)
How to determine whether lines are perpendicular.
1. Write each line in slope-intercept form.
2. Multiply the slopes together.
3. If the product is –1, then the lines are perpendicular.
![Page 6: 4-7B Perpendicular Lines Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649d0a5503460f949dcd0d/html5/thumbnails/6.jpg)
Write the equation of each line in the graph. Determine whether the lines are perpendicular.
x
y
Green line
y-intercept is 3
bmxy
3x23
y
Blue liney-intercept is –
1
32
slope
bmxy
1x32
y
1x32
y 1
32
23
The lines are perpendicular!
23
slope
•
• ••
These are
opposite reciproca
ls!
![Page 7: 4-7B Perpendicular Lines Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649d0a5503460f949dcd0d/html5/thumbnails/7.jpg)
Example 1 Write the equation of each line in the graph. Determine whether the lines are perpendicular.
x
y
Green liney-intercept is
3
bmxy 3xy
Blue liney-intercept is –
443
slope
bmxy
4x43
y
4x43
y
143
1
The lines are not perpendicular!
1 slope••
•
•
![Page 8: 4-7B Perpendicular Lines Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649d0a5503460f949dcd0d/html5/thumbnails/8.jpg)
Example 2 Write the equation of each line in the graph. Determine whether the lines are perpendicular.
x
y
Green liney-intercept is
1
bmxy
1x23
y
Blue liney-intercept is –
432
slope
bmxy
4x32
y
4x32
y 1
32
23
The lines are perpendicular!
23
slope •
•
••
![Page 9: 4-7B Perpendicular Lines Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649d0a5503460f949dcd0d/html5/thumbnails/9.jpg)
Write the slope-intercept form of an equation for the line that passes through (-4,-3) and is perpendicular to the graph of 4x + y = 2.
x
y
(-4,-3)
•
••
bmxy
b441
3
b441
3
Find the slope of the given line. 4m
Find the opposite reciprocal.
41
m
Use slope-intercept or point-slope to write the equation.
b13 11
b2
2x41
y
•
2yx4
![Page 10: 4-7B Perpendicular Lines Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649d0a5503460f949dcd0d/html5/thumbnails/10.jpg)
Write the slope-intercept form of an equation for the line that passes through (-4,-3) and is perpendicular to the graph of 4x + y = 2.
Find the slope of the given line. 4m
Find the opposite reciprocal. 4
1
Use slope-intercept or point-slope to write the equation.
bmxy
b441
3
b13 11
b2
2x41
y
11 xxmyy
4x41
3y
3 3
4x41
3y
1x41
3y
2x41
y
2yx4 x4 x4
2x4y
(when no graph is given)
![Page 11: 4-7B Perpendicular Lines Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649d0a5503460f949dcd0d/html5/thumbnails/11.jpg)
Example 3 Write the slope-intercept form of an equation for the line that passes through (-3,-2) and is perpendicular to the graph of x + 4y = 12.
Example 4 Write the slope-intercept form of an equation for the line that passes through (4,7) and is perpendicular to the graph of -2x + 3y = -3.
Example 5 Write the slope-intercept form of an equation for the line that passes through (4,-1) and is perpendicular to the graph of 7x - 2y = 3.
Find slope of given line.
Find the opposite reciprocal.
Use slope-intercept or point-slope form to write the equation.
![Page 12: 4-7B Perpendicular Lines Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649d0a5503460f949dcd0d/html5/thumbnails/12.jpg)
Example 3 Write the slope-intercept form of an equation for the line that passes through (-3,-2) and is perpendicular to the graph of x + 4y = 12.
Find slope of given line. 4
1m
Find the opposite reciprocal. 4
Use slope-intercept or point-slope form to write the equation.bmxy
b342
b122 1212
b1010x4y
11 xxmyy
3x42y
2 2
3x42y
12x42y
10x4y
12y4x x x
12xy4 4 4 4
3x41
y
![Page 13: 4-7B Perpendicular Lines Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649d0a5503460f949dcd0d/html5/thumbnails/13.jpg)
Example 4 Write the slope-intercept form of an equation for the line that passes through (4,7) and is perpendicular to the graph of -2x + 3y = -3.
Find slope of given line. 3
2m
Find the opposite reciprocal.
2
3
Use slope-intercept or point-slope form to write the equation.bmxy
b423
7
11 xxmyy
4x23
7y
7 7
4x23
7y
6x23
7y
13x23
y
3y3x2 x2 x2
3x2y3 3 3 3
1x32
y b67
66b13
13x23
y
![Page 14: 4-7B Perpendicular Lines Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649d0a5503460f949dcd0d/html5/thumbnails/14.jpg)
Example 5 Write the slope-intercept form of an equation for the line that passes through (4,-1) and is perpendicular to the graph of 7x - 2y = 3.
Find slope of given line. 2
7m
Find the opposite reciprocal. 7
2
Use slope-intercept or point-slope form to write the equation.bmxy
b472
1
11 xxmyy
4x72
1y
1 77
4x72
1y
78
x72
1y
71
x72
y
3y2x7 x7 x7
3x7y2 2 2 2
23
x27
y b
78
78
78
b71
71
x72
y
177
![Page 15: 4-7B Perpendicular Lines Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649d0a5503460f949dcd0d/html5/thumbnails/15.jpg)
Write an equation in slope-intercept form for a line perpendicular to the graph of -3x + 2y = 6 that passes through the x-intercept of the line.
What is the problem
asking you to do?x
y
•
-3x+2y=6
Write equation for
this line.
(but no graph is given)
![Page 16: 4-7B Perpendicular Lines Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649d0a5503460f949dcd0d/html5/thumbnails/16.jpg)
Write an equation in slope-intercept form for a line perpendicular to the graph of -3x + 2y = 6 that passes through the x-intercept of the line.
Find slope of given line. 2
3m
Find the opposite reciprocal.
32
Find the x-intercept of the given line. 6y2x3
602x3 6y2x3
x3 x36x3y2
2 2 2
3x23
y 336x3
2x
Use slope-intercept or point-slope form to write the equation.
Coordinate of x-intercept is (-2,0).
bmxy
b232
0
b34
0
34
34
b34
34
x32
y
![Page 17: 4-7B Perpendicular Lines Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649d0a5503460f949dcd0d/html5/thumbnails/17.jpg)
Write an equation in slope-intercept form for a line perpendicular to the graph of -3x + 2y = 6 that passes through the x-intercept of the line.
x
y
•
34
x32
y
![Page 18: 4-7B Perpendicular Lines Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649d0a5503460f949dcd0d/html5/thumbnails/18.jpg)
Example 6 Write an equation in slope-intercept form for a line perpendicular to the graph of x + 3y = 6 that passes through the x-intercept of the line.
Example 7 Write an equation in slope-intercept form for a line perpendicular to the graph of 3x + 2y = 8 that passes through the y-intercept of the line.
Find slope of given line.
Find the opposite reciprocal.
Use slope-intercept or point-slope form to write the equation.
Find the intercept of given line.
![Page 19: 4-7B Perpendicular Lines Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649d0a5503460f949dcd0d/html5/thumbnails/19.jpg)
Example 6 Write an equation in slope-intercept form for a line perpendicular to the graph of x + 3y = 6 that passes through the x-intercept of the line.
Find slope of given line. 3
1m
Find the opposite reciprocal.
3
Find the x-intercept of the given line. 6y3x
603x 6y3x
x x6xy3
3 3 3
2x31
y
6x
Use slope-intercept or point-slope form to write the equation.
Coordinate of x-intercept is (6,0).
bmxy
b630
b180 1818b18
18x3y
![Page 20: 4-7B Perpendicular Lines Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649d0a5503460f949dcd0d/html5/thumbnails/20.jpg)
Example 7 Write an equation in slope-intercept form for a line perpendicular to the graph of 3x + 2y = 8 that passes through the y-intercept of the line.
Find slope of given line. 2
3m
Find the opposite reciprocal. 3
2
Find the x-intercept of the given line. 8y2x3
8y203 8y2x3
x3 x38x3y2
2 2 2
4x23
y 228y2
4y
Use slope-intercept or point-slope form to write the equation.
Coordinate of y-intercept is (0,4).
bmxy
b032
4
b4
4x32
y
![Page 21: 4-7B Perpendicular Lines Algebra 1 Glencoe McGraw-HillLinda Stamper.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649d0a5503460f949dcd0d/html5/thumbnails/21.jpg)
4-A15 Pages 240-241 #18–25,28-30,36 and
Skills Practice Wkbk. Page 30 #13-24.Review nightly for trimester 1 exam.