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Parallel & Perpendicular Lines

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Presentation on theme: "Parallel & Perpendicular Lines"— Presentation transcript:

1 Parallel & Perpendicular Lines
Writing Equations of Parallel and Perpendicular Lines

2 Objectives Vocabulary parallel lines perpendicular lines
Identify and graph parallel and perpendicular lines. Write equations to describe lines parallel or perpendicular to a given line. Vocabulary parallel lines perpendicular lines

3 Parallel and Perpendicular
Remember parallel lines have the same slopes so if you need the slope of a line parallel to a given line, simply find the slope of the given line and the slope you want for a parallel line will be the same. Perpendicular lines have negative reciprocal slopes so if you need the slope of a line perpendicular to a given line, simply find the slope of the given line, take its reciprocal (flip it over) and make it negative.

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5 Helpful Hint If you know the slope of a line, the slope of a perpendicular line will be the "opposite reciprocal.”

6 Writing Equations of Parallel and Perpendicular Lines
Write an equation in slope-intercept form for the line that passes through (4, 10) and is parallel to the line described by y = 3x + 8. Step 1 Find the slope of the line. y = 3x + 8 The slope is 3. The parallel line also has a slope of 3. Step 2 Write the equation in point-slope form. y – y1 = m(x – x1) Use the point-slope form. Substitute 3 for m, 4 for x1, and 10 for y1. y – 10 = 3(x – 4)

7 Continued Write an equation in slope-intercept form for the line that passes through (4, 10) and is parallel to the line described by y = 3x + 8. Step 3 Write the equation in slope-intercept form. y – 10 = 3(x – 4) y – 10 = 3x – 12) Distribute 3 on the right side. y = 3x – 2 Add 10 to both sides.

8 Writing Equations of Parallel and Perpendicular Lines
Write an equation in slope-intercept form for the line that passes through (2, –1) and is perpendicular to the line described by y = 2x – 5. Step 1 Find the slope of the line. y = 2x – 5 The slope is 2. The perpendicular line has a slope of because Step 2 Write the equation in point-slope form. y – y1 = m(x – x1) Use the point-slope form. Substitute for m, –1 for y1, and 2 for x1.

9 Step 3 Write the equation in slope-intercept form.
Continued Write an equation in slope-intercept form for the line that passes through (2, –1) and is perpendicular to the line described by y = 2x – 5. Step 3 Write the equation in slope-intercept form. Distribute on the right side. Subtract 1 from both sides.

10 Try This! Write an equation in slope-intercept form for the line that passes through (5, 7) and is parallel to the line described by y = x – 6. Step 1 Find the slope of the line. The slope is . y = x –6 The parallel line also has a slope of Step 2 Write the equation in point-slope form. y – y1 = m(x – x1) Use the point-slope form.

11 Try This! Continued Write an equation in slope-intercept form for the line that passes through (5, 7) and is parallel to the line described by y = x – 6. Step 3 Write the equation in slope-intercept form. Distribute on the right side. Add 7 to both sides.

12 Try This! Write an equation in slope-intercept form for the line that passes through (–5, 3) and is perpendicular to the line described by y = 5x. Step 1 Find the slope of the line. y = 5x The slope is 5. The perpendicular line has a slope of because . Step 2 Write the equation in point-slope form. y – y1 = m(x – x1) Use the point-slope form.

13 Try This! Continued Write an equation in slope-intercept form for the line that passes through (–5, 3) and is perpendicular to the line described by y = 5x. Step 3 Write in slope-intercept form. Distribute on the right side. Add 3 to both sides.

14 Write an equation is slope-intercept form for the line described.
Try This! Write an equation is slope-intercept form for the line described. 1. contains the point (8, –12) and is parallel to 2. contains the point (4, –3) and is perpendicular to y = 4x + 5


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