Point-Slope Form Calculator
Enter a point and a slope below to instantly get the equation of the line.
Point-Slope Form
y − y₁ = m(x − x₁). Plug in the known point and slope directly — no solving required.
Worked example
Point (2, 5), slope 3.
Point-slope form: y − 5 = 3(x − 2)
Slope-intercept form: y − 5 = 3x − 6 → y = 3x − 1
A second example
Point (−4, −1), slope −2.
Point-slope form: y + 1 = −2(x + 4)
Slope-intercept form: y + 1 = −2x − 8 → y = −2x − 9
Keep going
- Point-slope and slope-intercept describe the same line, built from different starting information; the slope-intercept calculator builds it from two points and a y-intercept instead. Slope-Intercept Form Calculator
- Once you have a line's equation from point-slope form, solving it for a specific x is the next step; the linear equation calculator solves that equation directly. Linear Equation Calculator
Frequently Asked Questions
What is point-slope form?
Point-slope form writes a line's equation as y − y₁ = m(x − x₁), using one known point (x₁, y₁) and the slope m.
When is point-slope form more useful than slope-intercept form?
When you're given a point and a slope directly, point-slope form takes them with no extra algebra. You'd need an additional step to convert to slope-intercept form.
How do you convert point-slope form to slope-intercept form?
Distribute the slope and solve for y: y − y₁ = m(x − x₁) becomes y = mx − mx₁ + y₁, which simplifies to y = mx + b where b = y₁ − mx₁.
Where does point-slope form come from?
It comes directly from the slope formula. Since m = (y − y₁) / (x − x₁) for any point (x, y) on the line, multiplying both sides by (x − x₁) gives y − y₁ = m(x − x₁) — no extra points needed once you know one point and the slope.
What's a common mistake with point-slope form?
Dropping or flipping a sign when the known point has a negative coordinate. For a point like (−4, 2), the formula becomes y − 2 = m(x − (−4)), which simplifies to y − 2 = m(x + 4) — it's easy to accidentally write x − 4 instead.
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