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Name _______________________________________ Date ________________ Period______ Notes: Parallel and Perpendicular Lines Parallel Lines Perpendicular Lines SAME SLOPE but Different y-intercept y = 2x+1 m=2 Slopes are OPPOSITE RECIPROCALS y = 2x+1 y = 3 - ½x m=2 m=-½ y = 3+2x m=2 Horizontal Lines are parallel y = -2 y=8 m=0 m=0 Vertical and Horizontal Lines are perpendicular to each other y = -4 x=1 m = 0 m = undefined Vertical Lines are parallel x=3 x = -4 m = undefined m = undefined Identifying Parallel and Perpendicular Lines Ex1: Given the slope m = -2 , find the following: a) the slope of a parallel line m = ______ b) the slope of a perpendicular line m = ______ c) the slope of a line neither parallel or perpendicular m = ______ Your Turn Ex2: Given the slope m = 3/4 , find the following: a) the slope of a parallel line m = ______ b) the slope of a perpendicular line m = ______ c) the slope of a line neither parallel or perpendicular m = ______ Ex 3: What is the slope of… a) a line parallel to the line y = 3x + 2 m= b) a line perpendicular to the line y = -11 – 5x m= c) line perpendicular to the line x = 8 m= d) a line parallel to the line y = -x + 5 m= e) a line perpendicular to the line 3x - 2y = 4 m= Name: ______________________________________________ Date: _______________ Are the following lines parallel? 1. y 4x 2 y 9 4x 2. y 7 y 2 Are the following lines perpendicular? 5. y 5x 2 6. y 2x 1 1 y x4 y x4 5 2 3. y 1 x 6 2 2 x2 3 2x 3y 6 4. y 2x 4y 3 7. y x y x 9. y 4x 2 x 4y 8 8. y 3 x 3 In each box you will write in “Parallel to _________” or “Perpendicular to _________” y 4 x 1 5 x 3 1 y x4 2 1 y 2 x 3 y5 y 3x 4 2 y x 3 5 y 2 x 4 y 4x y 3x 1 y 3 x y 3 x 10 2 Identify which lines are parallel. Identify which lines are perpendicular. 1. Line1: 2x 5y 10 2 Line2 : y 5 Line3 : 4x 10y 20 2 Line4 : y x 1 5 2. Line1: y 6 x 7 7 Line2 : y x 2 6 Line3 : 7x 6y 14 6 Line4 : y x 2 7 Writing Equations Parallel and Perpendicular Lines Ex 1: Write the equation of the line with a y-intercept of 4 and perpendicular to y = 2x + 1. Step 1 Find the slope of the new line. Step 2 Write the equation in slope-intercept form using y = mx + b or y – y1 = m(x – x1). Ex 2: Write the equation of the line with a y-intercept of -2 and parallel to y = 4/5x. Step 1 Find the slope of the new line. Step 2 Write the equation in slope-intercept form using y = mx + b or y – y1 = m(x – x1). Ex 3: 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 new line. Step 2 Write the equation in slope-intercept form using y = mx + b or y – y1 = m(x – x1). Ex 4: 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 new line. Step 2 Write the equation in slope-intercept form using y = mx + b or y – y1 = m(x – x1). Ex 5: Write an equation in slope-intercept form for the line that passes through (5, 7) and is 4 parallel to the line described by y = x - 6 . 5 Step 1 Find the slope of the new line. Step 2 Write the equation in slope-intercept form using y = mx + b or y – y1 = m(x – x1). Ex 6: 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 new line. Step 2 Write the equation in slope-intercept form using y = mx + b or y – y1 = m(x – x1). Ex 7: Write an equation in slope-intercept form that is perpendicular to the graph and has a y-intercept of -3. Ex 8: The graph of a linear function f(x) is parallel to the line described by y = -½x – 1 and contains the point (-4, -1). What is the y-intercept of the linear function f(x)?