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Equations of Lines: Mastering Slopes & Forms

Practice and learn how to find slopes, equations, and determine parallel or perpendicular lines. Improve your geometry skills with clear examples and formulas.

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Equations of Lines: Mastering Slopes & Forms

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  1. Geometry Today: • Check Up • 3.4 Instruction • Practice Never discourage anyone who continually makes progress… no matter how slow. Plato

  2. Chapter 3 Check Up For 1 – 3, refer to the figure.

  3. 3.4 Equations of Lines Objectives: • Find the slope of lines • Find slope of parallel and perpendicular lines • Find equations of lines using y = mx + b • Find equations of lines using y – y1 = m(x – x1) • Write the equation of parallel lines Vocabulary: slope, slope intercept form, point-slope form

  4. 3.3 Slopes of Lines Formula: Slope rules: Parallel Lines: Perpendicular Lines: Parallel Lines: same slope opposite reciprocal slope y = # 0 slope: horizontal line x = # Undefined slope: vertical line

  5. 3.4 Equations of Lines Formulas: slope-intercept form y-intercept (0, b) slope Need slope (m) to find parallel and perpendicular from equation.

  6. Are these lines parallel, perpendicular or neither? L1 - (-3, 0), (4, 7) L2 - (5, 2), (2, -1) L3 - (1, -3), (-2, -1) L4 - (6, 0), (4, 3)

  7. Are these lines parallel, perpendicular or neither? y = 3x – 6 y = 3x+ 4 y = 1/5x + 4 y = 5x – 1/4 4y = 8x + 12 y = -1/2 x + 4 Perpendicular Need slope (m) to find parallel and perpendicular from equation.

  8. y1 x1 y - y1=m(x - x1) point (x1, y1) Formulas: point-slope form slope Used to find the equation of a line • find slope, m, and a point (x1, y1) • plug values into the equation • distribute and add

  9. y - y1=m(x - x1) • Find the equation of the line through (2, 5) and m = 3. y – 5 = 3 (x - 2) y1 x1 • Still distribute and add • Find the equation of the line through (0, 3) and parallel to y = 3x + 9. • Find the equation of the line through (4, -1) and perpendicular l to y = -2x – 1. m y1 x1 y1 x1 Perp m m = +½

  10. Are the 2 lines parallel, perpendicular, or neither? y = -2/3 x – 3 y = 2/3x + 5 3y + 4x = 24 4y – 3x = 12 4y + 3x = 15 12x + 9y = 36 Perp

  11. Find the equation of the line through (4, 5) and m = 6. • Find the equation of the line through (3, 7) and parallel to line from #1. • Find the equation of the line through (-2, 4) and perpendicular to line from #1. • Find the equation of the line through (-2, 4) and perpendicular to line y = 2x -7.

  12. Yesterday Assignment: • 3.4 p. 203 #37-55 odd, 59-61 all Never discourage anyone who continually makes progress… no matter how slow. Plato

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