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Graphing Parallel and Perpendicular Lines

Learn how to identify, graph, and write equations for parallel and perpendicular lines using slope-intercept form. Practice with examples and step-by-step instructions.

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Graphing Parallel and Perpendicular Lines

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  1. Warm Up • Identify which lines are parallel. • y = 6; y = 6x + 5; y = 6x – 7; y = -8 • Identify which lines are perpendicular • y = 3x – 4; y = x + 2; y = -1; x = 3

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

  3. Vocabulary parallel lines perpendicular lines

  4. Directions: Write an equation in slope-intercept form for the line that is parallel to the given line and that passes through the given point.

  5. Example 1 y = 3x + 8; (4, 10) Step 1 Find the slope of the line. The slope is 3. y = 3x + 8 The parallel line also has a slope of 3. Step 2 Write the equation in point-slope form. Use the point-slope form. y – y1 = m(x – x1) Substitute 3 for m, 4 for x1, and 10 for y1. y – 10 = 3(x – 4)

  6. Example 1 Continued 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.

  7. y = x – 6; (5, 7) The slope is . y = x –6 The parallel line also has a slope of . Example 2 Step 1 Find the slope of the line. Step 2 Write the equation in point-slope form. y – y1 = m(x – x1) Use the point-slope form.

  8. Distribute on the right side. Example 2 Continued Step 3 Write the equation in slope-intercept form. Add 7 to both sides.

  9. Directions: Write an equation in slope-intercept form for the line that is perpendicular to the given line and that passes through the given point.

  10. The perpendicular line has a slope of because Substitute for m, –1 for y1, and 2 for x1. Example 3 y = 2x – 5; (2, –1). Step 1 Find the slope of the line. y = 2x – 5 The slope is 2. Step 2 Write the equation in point-slope form. y – y1 = m(x – x1) Use the point-slope form.

  11. Distribute on the right side. Example 3 Continued Step 3 Write the equation in slope-intercept form. Subtract 1 from both sides.

  12. The perpendicular line has a slope of because . Example 4 y = 5x; (–5, 3) Step 1 Find the slope of the line. y = 5x The slope is 5. Step 2 Write the equation in point-slope form. y – y1 = m(x – x1) Use the point-slope form.

  13. Distribute on the right side. Example 4 Continued Step 3 Write in slope-intercept form. Add 3 to both sides.

  14. Lesson Summary 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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