Pointslope

Point-slope form is a form of the equation of a straight line that emphasizes a known point on the line and its slope. Given a line with slope m that passes through a point (x1, y1), its equation in point-slope form is y - y1 = m(x - x1).

From this form, you can graph the line directly or convert to other forms. Solving for y yields y = mx + b, where b = y1 - m x1, which is the slope-intercept form. If you know two points, you can compute the slope m = (y2 - y1)/(x2 - x1) and substitute into the point-slope equation with either point.

Example: a line of slope 3 through (2, 5) is y - 5 = 3(x - 2). This rearranges to y = 3x - 1. If the line is vertical, the slope is undefined and the equation is x = x1, which cannot be written in the standard point-slope form with a finite m.

Point-slope form is equivalent to other linear representations and is commonly used in solving and graphing linear equations, particularly when a point and the slope are known rather than the intercept.