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Point-Slope Form Calculator

Point-slope form, y − y₁ = m(x − x₁), is the quickest way to write a line when you know one point on it and its slope. Enter a point and a slope, or two points, and get the point-slope equation along with the same line as y = mx + b.

Quick examples

A fraction such as 2/3 works.

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Point-slope formy − 3 = 2(x − 1)
Slope-intercept form
y = 2x + 1
Slope (m)
2
y-intercept (b)
1

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      Formula

      y − y₁ = m(x − x₁)
      From two points: m = (y₂ − y₁) ÷ (x₂ − x₁)
      To slope-intercept form: b = y₁ − m × x₁

      How to use it

      1. Choose a point and slope, or two points.
      2. Enter the values. A slope can be typed as a fraction such as 2/3.
      3. Read the point-slope equation and its slope-intercept equivalent.

      Worked examples

      Through (1, 3) with slope 2

      Point-slope form
      y − 3 = 2(x − 1)
      Slope-intercept form
      y = 2x + 1
      y-intercept (b)
      1

      Through (−2, 5) and (4, −1)

      Point-slope form
      y − 5 = −(x + 2)
      Slope-intercept form
      y = −x + 3
      Slope (m)
      -1
      y-intercept (b)
      3

      Through (3, −4) with slope 0.5

      Point-slope form
      y + 4 = 0.5(x − 3)
      Slope-intercept form
      y = 0.5x − 5.5
      y-intercept (b)
      -5.5

      Watch the signs

      The form subtracts the point’s coordinates, so a negative coordinate turns into a plus. Through (−2, 5) with slope −1 the equation is y − 5 = −(x + 2), not y − 5 = −(x − 2).

      Many correct answers

      Any point on the line can be used, so the same line has many point-slope equations. Through (1, 3) and (4, 9), both y − 3 = 2(x − 1) and y − 9 = 2(x − 4) are right — each simplifies to y = 2x + 1.

      Questions people ask

      What is the point-slope form of a line through (1, 3) with slope 2?

      y − 3 = 2(x − 1), which simplifies to y = 2x + 1.

      How do I convert point-slope form to slope-intercept form?

      Distribute the slope and move the constant across: y − 3 = 2(x − 1) becomes y = 2x − 2 + 3, so y = 2x + 1.

      What if the two points are directly above each other?

      The line is vertical and has no slope, so there is no point-slope form. Its equation is x = the shared x-value.

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