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Slope-Intercept Form Calculator

Slope-intercept form, y = mx + b, shows a line’s slope and where it crosses the y-axis at a glance. Enter two points, or one point and the slope, to get the equation, both intercepts and the same line in standard form.

Quick examples
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Slope-intercept formy = 3x − 1
Slope (m)
3
y-intercept (b)
-1
x-intercept
0.3333
Standard form
3x − y = 1

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      Formula

      y = mx + b
      Slope: m = (y₂ − y₁) ÷ (x₂ − x₁)
      y-intercept: b = y₁ − m × x₁
      x-intercept = −b ÷ m
      Standard form: Ax + By = C

      How to use it

      1. Choose whether you have two points or a point and a slope.
      2. Enter the values. A slope can be typed as a fraction such as 2/3.
      3. Read the equation. To graph it, plot b on the y-axis, then move up m for every 1 to the right.

      Worked examples

      Through (1, 2) and (3, 8)

      Slope-intercept form
      y = 3x − 1
      Slope (m)
      3
      y-intercept (b)
      -1
      x-intercept
      0.3333
      Standard form
      3x − y = 1

      Through (0, 4) and (2, 0)

      Slope-intercept form
      y = −2x + 4
      Slope (m)
      -2
      y-intercept (b)
      4
      x-intercept
      2
      Standard form
      2x + y = 4

      Through (4, −2) with slope −0.5

      Slope-intercept form
      y = −0.5x
      y-intercept (b)
      0
      x-intercept
      0
      Standard form
      x + 2y = 0

      Through (2, 5) and (2, −1): a vertical line

      Slope-intercept form
      x = 2
      x-intercept
      2

      Reading m and b

      m is the slope: how much y changes when x increases by 1. b is the y-intercept: the value of y when x is 0. In y = 3x − 1, the line crosses the y-axis at −1 and climbs 3 for every step right.

      Lines it cannot describe

      A vertical line has no slope and never crosses the y-axis (or lies on top of it), so it cannot be written as y = mx + b. Its equation is x = a constant, which is what this calculator returns when both points share the same x.

      Questions people ask

      What is the equation of the line through (1, 2) and (3, 8)?

      The slope is 6 ÷ 2 = 3 and b = 2 − 3 × 1 = −1, so y = 3x − 1.

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

      Move the x term to the left and clear any fractions: y = 3x − 1 becomes 3x − y = 1.

      What is the slope-intercept form of a horizontal line?

      y = b. The slope is 0, so the x term vanishes; the line through (2, 4) and (7, 4) is y = 4.

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