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Mastering Equations of Lines: Point-Slope & Standard Forms

Learn how to write equations using point-slope form and convert to standard form with step-by-step instructions and examples. Understand the significance of slope in determining the equation of a line. Explore properties of parallel and perpendicular lines.

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Mastering Equations of Lines: Point-Slope & Standard Forms

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  1. Writing Equations of Lines Point Slope FormStandard Form

  2. Point Slope Form Variable Variable y – y1 = m(x – x1) Slope (x1, y1)

  3. Steps • Write the equation: • Determine the slope • Substitute slope for “m” • Substitute values from a point for x1 and y1 • Eliminate any “double signs” (i.e. +-, --, etc.)

  4. Why does the point-slope form work? Find the slope between (x1, y1) and (x, y). Reflexive property Point-Slope Form

  5. Write the equation of the line with slope 3 and passing through the point (1, 5). Use Point-Slope Form y – y1 = m(x – x1)

  6. Write the equation of the line with slope ¾ and passing through the point (-5, 3). Use Point-Slope Form y – y1 = m(x – x1)

  7. Write the equation of the line with slope -2/3 and passing through the point (2, -4). y – y1 = m(x – x1)

  8. Write the equation of the line passing through the points (-2, 6) and (3, -1). Find the slope y – y1 = m(x – x1) let's use (3, -1)

  9. Write the equation of the line passing through the points (4, 3) and (6, 8). Find the slope y – y1 = m(x – x1) let's use (4, 3)

  10. Write the equation of the line passing through the points (4, -3) and (-7, -1). Find the slope y – y1 = m(x – x1) let's use (4, -3)

  11. Standard Form Constant Both Can’t Be 0 Integer When Possible Any Constant

  12. Steps • Basically, solve for C • Get the “x” and “y” on one side of the = • Get the constant on the other side of the =

  13. Convert y = 3x + 2 to standard form. multiply both sides by -1

  14. Convert y = 6776x to standard form. multiply both sides by -4

  15. Convert y = 6776x to standard form. multiply both sides by 7

  16. Convert y = 6776x to standard form. multiply both sides by -2

  17. Convert y = 6776x to standard form. multiply both sides by 15

  18. More on Slope • Parallel lines have the same slope • Perpendicular lines have opposite reciprocal slopes Parallel Lines Perpendicular Lines

  19. Write the equation of the line parallel the line 4x – 5y = 7 that passes through the point (-3, 7) What is the slope of the given line? y – y1 = m(x – x1)

  20. Write the equation of the line perpendicular the line 3x + 2y = 9 that passes through the point (2, 5) What is the slope of the given line? y – y1 = m(x – x1)

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