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Page One We'll show you how to find the equation of any line, based on the information you know. The methods range from 'very easy' to 'quite complicated'. 1. You Know the Slope and Y Intercept eg: A line has slope 3 and y intercept -5. What is its equation? We covered this on the linear equations page. The answer is y = 3x - 5 eg: A line has slope -4 and passes through the point (0, 11). What is its equation? This is the same, as long as you recognize (0, 11) as the y intercept. The answer is y = -4x + 11 2. The Line is Horizontal or Vertical eg: A line passes through points (4, -2) and (4, 5) This is a vertical line at 4. Its equation is x = 4 eg: A line passes through points (-5, 6) and (1, 6) This is a horizontal line at 6. Its equation is y = 6 3. You Know Two Points, and One is the Y Intercept eg: A line passes through points (0, 2) and (3, 14) We have the y intercept. It's (0, 2) We don't know the slope, but with two points we can work it out: m = Δy over Δx = (14 - 2) over (3 - 0) = 12 over 3 = 4 With slope 4 and y intercept 2 the equation is y = 4x + 2 4. You Know the Y Intercept and a Hint About the Slope eg: A line passes through (0, -3) and is parallel to the line y = 7x + 1 The y intercept is -3 The line we want has the same slope, so it must be 7 The equation is y = 7x - 3 eg: A line passes through (0, 6) and is perpendicular to 12x - 6y = 11 We have the y intercept (0, 6) We need the slope of 12x - 6y = 11 This needs to be solved for y 12x - 6y = 11 - 6y = - 12x + 11 y = 2x - 11/6 This line has slope 2, so the line we want has a slope of -1/2 The equation is y = -1/2x + 6 Now let's find out what to do if you don't know the y intercept. Go to page two Linear Equations | Parallel and Perpendicular | Equation Forms | Finding Equations |