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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 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 • 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?
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.
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?
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?
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
Perpendicular lines are lines that form right angles. Find the slopes of the lines in each graph. Find the product of the slopes.
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
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.
homework • Pg253 # 1 – 4, 14 – 16, 25 - 27