1. Lesson 3-6 Part 2
Point-Slope Equation

2. 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)

3. 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

4. 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

5. Assignment
Textbook Page

6. 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

7. Assignment
Worksheet on Parallel and Perpendicular Lines from Equations.