Warm-Up 5 minutes 1. Graph the line y = 3x + 4.
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Transcript of Warm-Up 5 minutes 1. Graph the line y = 3x + 4.
![Page 1: Warm-Up 5 minutes 1. Graph the line y = 3x + 4.](https://reader036.fdocuments.in/reader036/viewer/2022082600/5a4d1af67f8b9ab05998192f/html5/thumbnails/1.jpg)
Warm-UpWarm-Up1. Graph the line y = 3x + 4.
5 minutes
2. Graph the line y = 3x - 23. What is the slope of the lines in the equations above?
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Parallel and Parallel and Perpendicular LinesPerpendicular Lines
Objectives: •To determine whether the graphs of two equations are parallel•To determine whether the graphs of two equations are perpendicular
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Parallel LinesParallel LinesParallel lines are lines in the same plane that never intersect.
-8 -6 -4 -2
2
42 6 8
4
6
-4
-6
-8
-2
8
Parallel lines have the same slope.
![Page 4: Warm-Up 5 minutes 1. Graph the line y = 3x + 4.](https://reader036.fdocuments.in/reader036/viewer/2022082600/5a4d1af67f8b9ab05998192f/html5/thumbnails/4.jpg)
Example 1Example 1Determine whether these lines are parallel.y = 4x -6
and y = 4x + 2
The slope of both lines is 4.So, the lines are parallel.
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Example 2Example 2Determine whether these lines are parallel.y – 2 = 5x + 4
and -15x + 3y = 9+2 +2
y = 5x + 6+15x +15x 3y = 9 +
15x3 3y = 3 + 5xy = 5x + 3
The lines have the same slope.So they are parallel.
![Page 6: Warm-Up 5 minutes 1. Graph the line y = 3x + 4.](https://reader036.fdocuments.in/reader036/viewer/2022082600/5a4d1af67f8b9ab05998192f/html5/thumbnails/6.jpg)
Example 3Example 3Determine whether these lines are parallel.y = -4x + 2 and -5 = -2y + 8x
+2y + 2y2y - 5 = 8x
+5 +52y = 8x + 52 2
5y 4x 2
Since these lines have different slopes, they are not parallel.
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PracticePractice
2) 3x – y = -5 and 5y – 15x = 10
Determine whether the graphs are parallel lines.
3) 4y = -12x + 16 and y = 3x + 4
1) y = -5x – 8 and y = 5x + 2
![Page 8: Warm-Up 5 minutes 1. Graph the line y = 3x + 4.](https://reader036.fdocuments.in/reader036/viewer/2022082600/5a4d1af67f8b9ab05998192f/html5/thumbnails/8.jpg)
Example 4Example 4Write the slope-intercept form of the equation of the line passing through the point (1, –6) and parallel to the line y = -5x + 3.
slope of new line =
-5y – y1 = m(x – x1)
y – (-6) = -5(x – 1)y + 6 = -5x +
5 y = -5x - 1
![Page 9: Warm-Up 5 minutes 1. Graph the line y = 3x + 4.](https://reader036.fdocuments.in/reader036/viewer/2022082600/5a4d1af67f8b9ab05998192f/html5/thumbnails/9.jpg)
PracticePracticeWrite the slope-intercept form of the equation of the line passing through the point (0,2) and parallel to the line 3y – x = 0.
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Practice 2Practice 2Determine whether the graphs of the equations are parallel lines.
1) 3x – 4 = y and y – 3x = 8
2) y = -4x + 2 and -5 = -2y + 8x
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Perpendicular LinesPerpendicular LinesPerpendicular lines are lines that intersect to form a 900 angle.
-8 -6 -4 -2
2
42 6 8
4
6
-4
-6
-8
-2
8
The product of the slopes of perpendicular lines is -1.
4m 22
2 1m 4 2
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Example 1Example 1Determine whether these lines are perpendicular.
and y = -3x - 21y x 73
1m 3 m = -31 33 1
Since the product of the slopes is -1, the lines are perpendicular.
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Example 2Example 2Determine whether these lines are perpendicular.
and y = -5x - 2
m 5 m = -55 5 25
Since the product of the slopes is not -1, the lines are not perpendicular.
y = 5x + 7
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PracticePracticeDetermine whether these lines are perpendicular.1) 2y – x = 2 and y = -2x + 4
2) 4y = 3x + 12 and -3x + 4y – 2 = 0
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Example 3Example 3Write an equation for the line containing (-3,-5) and perpendicular to the line y = 2x + 1.First, we need the slope of the line y = 2x + 1.
m = 2Second, we need to find out the slope of the line that is perpendicular to y = 2x + 1. 1m 2
Lastly, we use the point-slope formula to find our equation.
1 1(y y ) m(x x ) 1(y 5) (x 3)2
1y 5 (x 3)2
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PracticePracticeWrite an equation for the line containing the given point and perpendicular to the given line.1) (0,0); y = 2x + 4
2) (-1,-3); x + 2y = 8