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5-8 parallel and perpendicular lines

5-8 parallel and perpendicular lines. Miss battaglia – algebra 1 CP Objective: Write equations for parallel and perpendicular lines; use slope to determine if lines are parallel, perpendicular, or neither. Warm up.

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5-8 parallel and perpendicular lines

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  1. 5-8 parallel and perpendicular lines Miss battaglia – algebra 1 CP Objective: Write equations for parallel and perpendicular lines; use slope to determine if lines are parallel, perpendicular, or neither.

  2. Warm up • A 12 ft square patio is built in a 25 ft by 35 ft rectangular backyard. How many square feet of the backyard are not covered by the patio?

  3. Work with a partner • Match each story with its graph. Explain your choices. • Elena gives her younger sister Rosa a head start in a race. Elena rushes faster than her sister. • Elena gives her younger sister Rosa a head start in a race. Elena is surprised that she and her sister run at the same rate. • A. B.

  4. Think & discuss • How far apart are the two runners at 0s? 1s? 2s? 3s? • Suppose the race were longer and the pattern for the distance between runners remained the same. Would the lines intersect? • What is the slope of each line in the graph?

  5. Think & discuss • Two parallel lines are always the same distance apart. They do not intersect. • Slopes of Parallel Lines • Nonvertical lines are parallel if they have the same slope and different y-intercepts. Vertical lines are parallel. • Ex: y = 2x + 3 and y = 2x – 5 are parallel. Are horizontal lines parallel? What is the slope of a line parallel to y=x –4?

  6. example • Write an equation for a line that contains (-2,3) and is parallel to the graph of 5x-2y=8. • Step 1: Find the slope of 5x-2y=8 • Step 2: Use slope-intercept form to find the y-intercept

  7. Perpendicular lines are lines that form right angles. Find the slopes of the lines in each graph. Find the product of the slopes.

  8. Slope of perpendicular lines • Two lines are perpendicular if the product of their slopes is -1. A vertical and a horizontal line are perpendicular. • Ex: y = -4x+7 and y = x + 2 are perpendicular. • Find the slope of a line perpendicular to a line with this slope. • a. -2 b. c. undefined

  9. Urban planning • A bike path for a new city park will connect the park entrance to Park Road. The path will be perpendicular to Park Road. Write an equation for the line representing the bike path.

  10. homework • Pg253 # 1 – 4, 14 – 16, 25 - 27

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