3.7-3.8 equations of lines in the coordinate plane and slopes of parallel and perpendicular lines

3.7-3.8 Equations of Lines in 3.7-3.8 Equations of Lines in the Coordinate Plane and the Coordinate Plane and Slopes of Parallel and Slopes of Parallel and Perpendicular LinesPerpendicular Lines

Objective: Students will find the slopes of Objective: Students will find the slopes of lines and use slope to identify parallel lines and use slope to identify parallel and perpendicular lines.and perpendicular lines.

Definitions and Definitions and PostulatesPostulates

SlopeSlope::

Two nonvertical lines have the same slope if Two nonvertical lines have the same slope if and only if they are paralleland only if they are parallel

Two nonvertical lines are perpendicular if and Two nonvertical lines are perpendicular if and only if the product of their slopes is -1only if the product of their slopes is -1 Slopes are opposite reciprocals.Slopes are opposite reciprocals.

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ExamplesExamples

Find the slope of each line.Find the slope of each line.1. (-3,7) and (-1,-1)1. (-3,7) and (-1,-1)2. (0,4) and (0,-3)2. (0,4) and (0,-3)3. (-2,-1) and (6,-1)3. (-2,-1) and (6,-1)

Determine whether line FG and line HJ are Determine whether line FG and line HJ are parallel, perpendicular, or neither.parallel, perpendicular, or neither.1. F(-1,3), G(-2,-1), H(5,0), J(6,3)1. F(-1,3), G(-2,-1), H(5,0), J(6,3)2. F(4,2), G(6,-3), H(-1,5), J(-3,10)2. F(4,2), G(6,-3), H(-1,5), J(-3,10)3. F(-3,-2), G(9,1), H(3,6), J(5,-2)3. F(-3,-2), G(9,1), H(3,6), J(5,-2)

Equations of LinesEquations of Lines

Slope-Intercept Form: Slope-Intercept Form: where m = slope and b = y-interceptwhere m = slope and b = y-intercept

Point-Slope Form: Point-Slope Form: where m = slope, y1 = y coordinate, x1 = x where m = slope, y1 = y coordinate, x1 = x coordinate.coordinate.

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Writing equations given a Writing equations given a slope and a y-interceptslope and a y-intercept

Write an equation in slope-intercept Write an equation in slope-intercept form for the given information.form for the given information.

1.1. m = 6, y-intercept = -3m = 6, y-intercept = -3

2.2. m = -1/2 , y-intercept = 4m = -1/2 , y-intercept = 4

Write an equation of a Write an equation of a line given a slope and a line given a slope and a pointpoint

Write an equation in point-slope and Write an equation in point-slope and slope-intercept form using the given slope-intercept form using the given information.information.

1.1. m = -3/5, (-10,8)m = -3/5, (-10,8)

2.2. m = 3, (4,-1)m = 3, (4,-1)

Write an equation of a Write an equation of a line given 2 pointsline given 2 points

Write an equation of the line in slope-Write an equation of the line in slope-intercept form given 2 points.intercept form given 2 points.

1.1. (4,9) and (-2,0)(4,9) and (-2,0)

2.2. (3,-1), (7,-1)(3,-1), (7,-1)

3.3. (2,5), (2,-10)(2,5), (2,-10)

Write equations of Write equations of parallel and parallel and perpendicular linesperpendicular lines

Write an equation in slope-intercept Write an equation in slope-intercept form for the given information.form for the given information.

1.1. A line parallel to A line parallel to and and contains (7,-2).contains (7,-2).

2.2. A line perpendicular toA line perpendicular to and and contains (-2,-3).contains (-2,-3).

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