Lesson 3-6 Part 2 Point-Slope Equation

Point-Slope Equation Slope-Intercept and Table methods allow you to graph a line if given an equation. The point-slope equation performs the reverse, you use it to get a linear equation from a line. Given a slope, m, and a point the line passes through (x1, y1): y - y1 = m(x - x1)

Point-Slope Equation Examples Ex. What is the equation of a line with a slope of ¾, that passes through (4, 1)? y – 1 = ¾(x – 4) y – 1 = ¾x – 3 y = ¾x – 2 Ex. What is the equation of a line with a slope of -½, that passes through (-7, 3)? y – 3 = -½ (x – -7) y – 3 = -½x – 3½ y = -½x – ½

Point-Slope with Two Points. Calculate the slope between the points using the slope formula, and then use the slope and either of the two points in the point-slope equation. Ex. (1, 0) and (0, -3) m = (-3 – 0)/(0 – 1)  m = 3 y – -3 = 3(x – 0) y + 3 = 3x y = 3x – 3

Assignment Textbook Page 169 17-28.

Point-Slope with a Point and Parallel or Perpendicular. Parallel  equal slope with another line. Perpendicular  opposite and reciprocal slope with another line (flip fraction and sign). Ex. What’s the equation of a line through (2, -1) and perpendicular to a line with a slope of -½? perpendicular line  m = +2 y – -1 = 2(x – 2) y + 1 = 2x – 4 y = 2x – 5

Assignment Worksheet on Parallel and Perpendicular Lines from Equations.