Point-Slope Form Calculator
This calculator converts point-slope form to slope-intercept form. Given a point (x1, y1) and the slope m, the tool displays the equation in both point-slope form (y - y1 = m(x - x1)) and slope-intercept form (y = mx + b). Point-slope form is especially useful when you have a point and a slope but do not yet know the y-intercept.
Point-slope form
Point-slope form: y - y1 = m(x - x1)
where m is the slope and (x1, y1) is a known point
Converted to slope-intercept: y = mx + b
where b = y1 - m*x1
Point-slope form: frequently asked questions
What is point-slope form?
Point-slope form is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a known point on the line. This form is useful when you know the slope and a point, as it directly incorporates both pieces of information.
How do I convert point-slope form to slope-intercept form?
Expand the equation y - y1 = m(x - x1) to get y - y1 = mx - mx1, then solve for y: y = mx - mx1 + y1, which is y = mx + b where b = y1 - mx1.
When should I use point-slope form?
Use point-slope form when you are given the slope and a point on the line. It is more convenient than slope-intercept form in this situation because you do not need to first calculate the y-intercept.
How do I use this calculator?
Enter the coordinates (x1, y1) of a known point and the slope m. The calculator displays the equation in both point-slope form and slope-intercept form.
Can point-slope form represent a vertical line?
No, point-slope form requires a slope, which is undefined for vertical lines. For a vertical line, the equation is simply x = x1 (a constant x value).
Methodology
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.