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Linear Equations Straight Lines

Slope of y = mx b. For the line given by the equation y = mx b,the number m is called the slope of the line. . Example: Slope of y = mx b. Find the slope. y = 6x - 9 y = -x 4 y = 2 y = x. Geometric Definition of Slope. Geometric Definition of Slope Let L be a line pa

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Linear Equations Straight Lines

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    1. Linear Equations & Straight Lines The Slope of a Straight Line

    2. Slope of y = mx + b For the line given by the equation y = mx + b, the number m is called the slope of the line.

    3. Example: Slope of y = mx + b Find the slope. y = 6x - 9 y = -x + 4 y = 2 y = x

    4. Geometric Definition of Slope Geometric Definition of Slope Let L be a line passing through the points (x1,y1) and (x2,y2) where x1 ? x2. Then the slope of L is given by the formula

    5. Example Use the geometric definition of slope to find the slope of y = 6x - 9.

    6. Point-Slope Formula Point-Slope Formula The equation of the straight line through the point (x1,y1) and having slope m is given by y - y1 = m(x - x1).

    7. Example: Point-Slope Formula Find the equation of the line through the point (-1,4) with a slope of .

    8. Perpendicular Property Perpendicular Property When two lines are perpendicular, their slopes are negative reciprocals of one another. That is, if two lines with slopes m and n are perpendicular to one another, then m = -1/n. Conversely, if two lines have slopes that are negative reciprocals of one another, they are perpendicular.

    9. Example: Perpendicular Property Find the equation of the line through the point (3,-5) that is perpendicular to the line whose equation is 2x + 4y = 7.

    10. Parallel Property Parallel Property Parallel lines have the same slope. Conversely, if two lines have the same slope, they are parallel.

    11. Example: Parallel Property Find the equation of the line through the point (3,-5) that is parallel to the line whose equation is 2x + 4y = 7.

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