Understanding Line Equations and Relationships
Explore the concepts of point-slope form, slopes, parallel and perpendicular lines, and equations of lines parallel or perpendicular to given lines. Discover how to calculate slopes and write equations in various forms efficiently.
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Presentation Transcript
Chapter 2 Section 5 The Point-Slope Form of the Equation of a Line
Point-Slope Form Nonvertical line with slope, m, that passes through the point (?1,?1) ? ?1= ?(? ?1)
Find Slope and a point on the line. 1) y 5 = 7(x 4) 2) y + 3 = 7 3(x 1) 3) y 1 = 2(x + 3)
Write the equation of a line Point-Slope Form and Slope-Intercept Form a) Slope = 4 passing through (3, 1) b) Passing through (1, 3) and (2, 4) c) Passing through (- 4, 5) with x-intercept of 3
Parallel Lines What do you know about parallel lines? What about the slopes?
Perpendicular lines Two lines are perpendicular of the product of their slopes is -1 To find the slope of a perpendicular line, take the slope of the line and find the negative reciprocal.
Parallel, Perpendicular If the slope of a line is 2 5 The slope of the parallel line is: The slope of the perpendicular line is:
Find the slope of a line parallel and perpendicular to d) 4x + y = 11
Write the equation of a line Parallel and perpendicular to d) 3x + 2y = 6 2 5x-1 e) y = - ? ?
Summary Write an equation in point-slope form Write an equation in standard form Find slopes of parallel and perpendicular lines Write equations of a line that are parallel and perpendicular to a given line
