Lines in the Plane Property of Texas Tech University

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Presentation transcript:

Lines in the Plane Property of Texas Tech University Department of Mathematics & Statistics

Slope The slope of a line is more than just a formula, it tells you how fast 𝑦 is changing. It is a rate of change.

Slope-Intercept Form 𝑚 is the slope of the line. (0,𝑏) is the y-intercept of the line.

Point-Slope Form 𝑚 is the slope of the line. (𝑥1,𝑦1) is a point on the line

Special Lines Horizontal lines have m=0. So the equation of the line is Vertical lines have an undefined slope. So the equation of the line is

Parallel and Perpendicular Lines Two lines are parallel if and only if their slopes are the same. Two lines are perpendicular if and only if the product of their slopes is −1.

Find the equation of the line perpendicular to 2𝑥 −3𝑦 = 1 and passing through 4,2 . Solution Any line perpendicular to this one must have slope

Find the equation of the line perpendicular to 2𝑥 −3𝑦 = 1 and passing through 4,2 . We want a line with slope through (4,2). It follows that