Point-Slope Form

If you know the slope m and one point (x_1, y_1) on the line, you can write the equation as: [formula] This is often the fastest way to write an equation when you're given a point and a slope (or two points). Why it works: it's just the slope formula rearranged: [formula]

Example: Write the equation of a line with slope 3 through (2, 5) in point-slope form.

The SAT may give you one form and ask for another: | Form | Equation | Best for | |---|---|---| | Slope-intercept | y = mx + b | Reading slope and y-intercept | | Point-slope | y - y_1 = m(x - x_1) | Writing equations quickly | | Standard | Ax + By = C | Finding x and y intercepts | To convert point-slope → slope-intercept: distribute and simplify. To convert slope-intercept → standard: move th…