Parallel and Perpendicular Lines Objectives: Define parallel lines. Find equations of parallel...
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Transcript of Parallel and Perpendicular Lines Objectives: Define parallel lines. Find equations of parallel...
![Page 1: Parallel and Perpendicular Lines Objectives: Define parallel lines. Find equations of parallel lines. Define perpendicular lines Find equations of perpendicular.](https://reader036.fdocuments.net/reader036/viewer/2022082417/56649d0a5503460f949dccc6/html5/thumbnails/1.jpg)
Parallel and Parallel and Perpendicular Perpendicular
LinesLinesObjectives: Define parallel lines.Objectives: Define parallel lines.Find equations of parallel lines.Find equations of parallel lines.
Define perpendicular linesDefine perpendicular linesFind equations of perpendicular lines.Find equations of perpendicular lines.
![Page 2: Parallel and Perpendicular Lines Objectives: Define parallel lines. Find equations of parallel lines. Define perpendicular lines Find equations of perpendicular.](https://reader036.fdocuments.net/reader036/viewer/2022082417/56649d0a5503460f949dccc6/html5/thumbnails/2.jpg)
Parallel LinesParallel Lines• Slopes of parallel lines are equal.
• Recall the steps of finding an equation of a line.– Find slope– Find the y-intercept– Write the equation
– This is the same process when working with parallel and perpendicular lines.
![Page 3: Parallel and Perpendicular Lines Objectives: Define parallel lines. Find equations of parallel lines. Define perpendicular lines Find equations of perpendicular.](https://reader036.fdocuments.net/reader036/viewer/2022082417/56649d0a5503460f949dccc6/html5/thumbnails/3.jpg)
Find an equation of a line Find an equation of a line passing through (-2,5) that is passing through (-2,5) that is
parallel to parallel to 3x + 2y = 93x + 2y = 9
• Find slope:– Get y by itself in the given equation
2y = 9 – 3x y = 9/2 – 3/2 x slope=-3/2
• Find y-intercept:– Use a slope of -3/2 since the lines are parallely = -3/2 x + b 5 = -3/2 (-2) + b 5 = 3 + b2 = b
• Write equation:y = -3/2 x + 2
![Page 4: Parallel and Perpendicular Lines Objectives: Define parallel lines. Find equations of parallel lines. Define perpendicular lines Find equations of perpendicular.](https://reader036.fdocuments.net/reader036/viewer/2022082417/56649d0a5503460f949dccc6/html5/thumbnails/4.jpg)
Perpendicular LinesPerpendicular Lines• Perpendicular lines have negative
reciprocal slopes.• If a line has a slope of -1/2 the
perpendicular line would have a slope of 2.• If a line has a slope of 5/6 the
perpendicular line would have a slope of -6/5
• What would be the slope of a line perpendicular to a line with a slope of -7?
1/7
![Page 5: Parallel and Perpendicular Lines Objectives: Define parallel lines. Find equations of parallel lines. Define perpendicular lines Find equations of perpendicular.](https://reader036.fdocuments.net/reader036/viewer/2022082417/56649d0a5503460f949dccc6/html5/thumbnails/5.jpg)
Find the equation of the line Find the equation of the line passing through (-1,3) that is passing through (-1,3) that is perpendicular to 3x – 2y = 8.perpendicular to 3x – 2y = 8.
1. Find slope1. Get y by itself: -2y = 8 – 3x y = -4 +
3/2 x2. Slope is 3/2 so perpendicular slope is -
2/3
2. Find y-intercept1. y = -2/3 x + b 3 = (-2/3)(-1) + b
3 = 2/3 + b 3 – 2/3 = b 7/3 = b
3. Write equationy = -2/3 x + 7/3
![Page 6: Parallel and Perpendicular Lines Objectives: Define parallel lines. Find equations of parallel lines. Define perpendicular lines Find equations of perpendicular.](https://reader036.fdocuments.net/reader036/viewer/2022082417/56649d0a5503460f949dccc6/html5/thumbnails/6.jpg)
Review concepts learnedReview concepts learned• Parallel lines have equal slope• Perpendicular lines have negative
reciprocal slopes.• To find an equation of a line
– Find slope– Find y-intercept– Write equation
![Page 7: Parallel and Perpendicular Lines Objectives: Define parallel lines. Find equations of parallel lines. Define perpendicular lines Find equations of perpendicular.](https://reader036.fdocuments.net/reader036/viewer/2022082417/56649d0a5503460f949dccc6/html5/thumbnails/7.jpg)
AssignmentAssignment• Page 197• #7, 11, 13, 17, 21, 23, 25, 29, 33, 37