Point-Slope Form Calculator
Point-slope form writes a line straight from one point and its slope: through (1, 2) with slope 3 it is y − 2 = 3(x − 1).
y − 2 = 2(x − 1)
- Slope-intercept form
- y = 2x
- Standard form
- 2x − y = 0
- Slope m
- 2
- y-intercept b
- 0
Step-by-step solution
- y − y₁ = m(x − x₁) with (x₁, y₁) = (1, 2) and m = 2
- y − 2 = 2(x − 1)
- Expand: y = 2x
Point-Slope Form Formula
y − y₁ = m(x − x₁)
point (x₁, y₁), slope m
Worked Example
The line through (1, 2) with slope 3:
- y − y₁ = m(x − x₁) with (x₁, y₁) = (1, 2) and m = 3
- y − 2 = 3(x − 1)
- Expand: y = 3x − 1
Standard form: 3x − y = 1 · Slope m: 3 · y-intercept b: -1
Test-day tip
SAT answer choices are often in different forms. Expand point-slope form to y = mx + b to compare choices quickly, or graph each choice in the built-in calculator and see which one passes through the given point.
More Algebra Calculators
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Slope Calculator
m = (y₂ − y₁) ÷ (x₂ − x₁)
rise over run between points (x₁, y₁) and (x₂, y₂)
Example: The line through (1, 2) and (4, 8): Slope m = 2.
-
Slope-Intercept Form Calculator
y = mx + b
m slope, b y-intercept = y₁ − m·x₁
Example: The line through (1, 2) and (4, 8): Slope-intercept form: y = 2x.
-
Systems of Equations Calculator
a₁x + b₁y = c₁, a₂x + b₂y = c₂
solved by elimination / Cramer’s rule; determinant 0 means no unique solution
Example: The system 2x + 3y = 12 and x − y = 1: Solution: x = 3, y = 2.
-
Linear Inequality Calculator
ax + b < c → x < (c − b)/a
the inequality sign reverses when dividing by a negative a
Example: The inequality −3x + 4 < 10: Solution = x > -2.
Frequently asked questions
When is point-slope form most useful?
When you know a point and the slope but not the y-intercept, for example a tangent line or a line through a given point parallel to another.
Is point-slope form unique?
No. Any point on the line gives a valid point-slope equation; they all expand to the same y = mx + b.
Sources
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Point-Slope Form Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/point-slope-form-calculator/
IEEE
Scientific Converters, "Point-Slope Form Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/point-slope-form-calculator/