Definition: Point-slope form writes a line as y – y1 = m(x – x1), using the slope m and any one known point (x1, y1) on the line.
When is point-slope form handy?
Use it when the problem hands you a slope and one point, or two points from which you can compute the slope. You can write the equation immediately, with no solving for an intercept.
How do you build the equation?
Substitute the slope for m and the coordinates of the point for x1 and y1. Watch the signs: subtracting a negative coordinate turns into addition.
Example. A line passes through (-3, 8) and (5, 0). The slope is (0 – 8) / (5 – (-3)) = -8/8 = -1. Using the point (5, 0), the equation is y – 0 = -1(x – 5). Using (-3, 8) instead gives y – 8 = -1(x + 3). Both simplify to y = -x + 5, so the choice of point does not matter.
What goes wrong?
A common slip is writing y + 8 when the point has y = 8, or copying x1 without its sign. Check by plugging your point back in: both sides must be zero or equal. Also remember the form is not unique, so two different-looking answers can describe the same line.