Point-Slope Form Calculator

The point-slope form of a line is y − y₁ = m(x − x₁), where m is the slope and (x₁, y₁) is a point on the line. This calculator builds that equation from your point and slope, rearranges it into slope-intercept form y = mx + c and standard form Ax + By = C with whole numbers, and graphs the line.

Try:

How to use the point-slope form calculator

  1. Enter the point (x₁, y₁).
  2. Enter the slope m, such as 2 or 3/2.
  3. Press Calculate to see all three forms and the graph.

Formula

y−y1=m(x−x1)y - y_1 = m(x - x_1)
y=mx+cy = mx + c

Worked example: (2, −1), m = 3/2

  • x₁: 2
  • y₁: -1
  • Slope m: 3/2

✓ Answer checked

y=32x−4y = \frac{3}{2}x - 4
Point-slope form
y+1=32(x−2)y + 1 = \frac{3}{2}\left(x - 2\right)
Standard form
3x−2y=83x - 2y = 8
y-intercept
(0,  −4)(0,\; -4)
−3−2−112345−8−6−4−224(2, -1)y-interceptline
A line through (2, -1) rising 3/2 for every 1 across.
Step-by-step working (3 steps)

  1. Point-slope form Point-slope form

    Put the point and slope into y − y₁ = m(x − x₁).

    y+1=32(x−2)y + 1 = \frac{3}{2}\left(x - 2\right)

  2. Expand and rearrange Slope-intercept form y = mx + c

    Multiply out and add y₁ to both sides.

    y=32x−4y = \frac{3}{2}x - 4

  3. Standard form

    Clear fractions and collect x and y on one side.

    3x−2y=83x - 2y = 8
Formulas used
y−y1=m(x−x1)y - y_1 = m(x - x_1)
y=mx+cy = mx + c
How this was checked
  • ✓ The point lies exactly on the line.

Frequently asked questions

What is the equation of the line through (2, −1) with slope 3/2?

y + 1 = 3/2 (x − 2), which simplifies to y = 3/2 x − 4.

What is standard form?

Ax + By = C with whole numbers, such as 3x − 2y = 8.

What if I have two points instead?

Use the slope calculator, which finds the slope and the equation from two points.

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