Point Slope Form Calculator

Point-slope form formula

Point-slope form is useful when you know a point on a line and the slope of the line. OpenStax gives the point-slope form as y − y₁ = m(x − x₁) in its lesson on finding the equation of a line.

Worked example

Why point-slope form is often easier

If a problem gives you a point and a slope, point-slope form avoids solving for the y-intercept first. After writing the point-slope equation, you can expand it into slope-intercept form or standard form if the teacher asks for a different final format.

Common questions

• What is point-slope form?
  Point-slope form is y - y1 = m(x - x1), where m is slope and (x1, y1) is a point on the line.
• When should I use point-slope form?
  Use it when you know one point on a line and the slope, or when you can find the slope from two points.
• How do I convert point-slope to slope-intercept form?
  Distribute the slope, then solve for y.
• Can a vertical line use point-slope form?
  A vertical line has undefined slope, so it is usually written as x = a instead.
• Can a horizontal line use point-slope form?
  Yes. Its slope is 0, so the equation simplifies to y = y1.
• Which point should I use if I have two points?
  Either point works if the slope is correct. The final line is the same.
• Is point-slope form a final answer?
  Usually yes, unless the problem specifically asks for slope-intercept or standard form.
• Why are there minus signs in the formula?
  The formula is based on slope as change in y over change in x from a known point.