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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 the Coordinate Plane and Slopes of Parallel and Perpendicular Lines. Objective: Students will find the slopes of lines and use slope to identify parallel and perpendicular lines. Definitions and Postulates. Slope :

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

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  1. 3.7-3.8 Equations of Lines in the Coordinate Plane and Slopes of Parallel and Perpendicular Lines Objective: Students will find the slopes of lines and use slope to identify parallel and perpendicular lines.

  2. Definitions and Postulates • Slope: • Two nonvertical lines have the same slope if and only if they are parallel • Two nonvertical lines are perpendicular if and only if the product of their slopes is -1 • Slopes are opposite reciprocals.

  3. Examples • Find the slope of each line. 1. (-3,7) and (-1,-1) 2. (0,4) and (0,-3) 3. (-2,-1) and (6,-1) • Determine whether line FG and line HJ are parallel, perpendicular, or neither. 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) 3. F(-3,-2), G(9,1), H(3,6), J(5,-2)

  4. Equations of Lines • Slope-Intercept Form: where m = slope and b = y-intercept • Point-Slope Form: where m = slope, y1 = y coordinate, x1 = x coordinate.

  5. Writing equations given a slope and a y-intercept • Write an equation in slope-intercept form for the given information. • m = 6, y-intercept = -3 • m = -1/2 , y-intercept = 4

  6. Write an equation of a line given a slope and a point • Write an equation in point-slope and slope-intercept form using the given information. • m = -3/5, (-10,8) • m = 3, (4,-1)

  7. Write an equation of a line given 2 points • Write an equation of the line in slope-intercept form given 2 points. • (4,9) and (-2,0) • (3,-1), (7,-1) • (2,5), (2,-10)

  8. Write equations of parallel and perpendicular lines • Write an equation in slope-intercept form for the given information. • A line parallel to and contains (7,-2). • A line perpendicular to and contains (-2,-3).

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