Point Slope Form Calculator – Guide & Formulas
Convert point-slope form to slope-intercept and standard form. Enter a point and slope to get the full line equation with step-by-step solutions.
Convert point-slope form equations into slope-intercept and standard form. Enter a point (x₁, y₁) and slope m to instantly see all forms of the line equation, including x-intercept, y-intercept, and a step-by-step derivation.
Key Takeaway
Use the free Point Slope Form Calculator to convert point-slope form to slope-intercept and standard form. enter a point and slope to get the full line equation with step-by-step solutions. Get instant results with step-by-step explanations.
How to Use the Point Slope Form Calculator
- Enter the x-coordinate of the point (x₁).
- Enter the y-coordinate of the point (y₁).
- Enter the slope (m) of the line.
- Review all equation forms: point-slope, slope-intercept, and standard form.
The Formula
Variable Definitions
- m: Slope of the line (rise over run)
- x₁: x-coordinate of the given point
- y₁: y-coordinate of the given point
- b: y-intercept in slope-intercept form (b = y₁ - mx₁)
Line through (3, 5) with slope m = 2
Write the equation of a line passing through (3, 5) with slope 2.
- Step 1: Substitute into point-slope form: y - 5 = 2(x - 3).
- Step 2: Distribute the slope: y - 5 = 2x - 6.
- Step 3: Add 5 to both sides: y = 2x - 1 (slope-intercept form).
- Step 4: y-intercept is (0, -1). x-intercept: set y = 0 → 0 = 2x - 1 → x = 0.5, so (0.5, 0).
Frequently Asked Questions
What is point-slope form?
Point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) is a known point on the line and m is the slope. It is the most direct way to write a line equation when you know a point and the slope.
How do I convert point-slope to slope-intercept form?
Distribute the slope m on the right side, then add y₁ to both sides to isolate y. The result is y = mx + (y₁ - mx₁), where the y-intercept b = y₁ - mx₁.
What if the slope is undefined (vertical line)?
A vertical line through (x₁, y₁) has equation x = x₁. It cannot be written in slope-intercept or point-slope form because the slope is undefined (infinite).
What if the slope is zero (horizontal line)?
A horizontal line through (x₁, y₁) has equation y = y₁. In point-slope form this becomes y - y₁ = 0(x - x₁), which simplifies to y = y₁.
How do I convert to standard form Ax + By = C?
From slope-intercept y = mx + b, rearrange to mx - y = -b. Multiply through to clear fractions if needed so A, B, C are integers with A ≥ 0.
When should I use point-slope form?
Use point-slope form when you know a point on the line and its slope, or when you can easily compute the slope from two points. It is the fastest form to write directly from given information.
Can two different points give the same point-slope equation?
Yes, a line can be written in point-slope form using any point on the line. All such forms are equivalent and convert to the same slope-intercept equation.
What is the relationship between slope and angle of inclination?
The slope m equals tan(θ), where θ is the angle the line makes with the positive x-axis. For example, m = 1 corresponds to θ = 45°, and m = 0 corresponds to θ = 0° (horizontal).