Point Slope Form Calculator
Convert between point-slope form and other line equation forms with step-by-step solutions
Point-Slope Form Calculator
Point and Slope
Line Equation Forms
Point-Slope Form
y + 3 = 2(x - 2)
General form: y - y₁ = m(x - x₁)
Slope-Intercept Form
y = 2x -7
General form: y = mx + b
Standard Form
2x -1y -7 = 0
General form: Ax + By + C = 0
Line Properties
Step-by-Step Solution
1. Start with the point-slope form
General formula: y - y₁ = m(x - x₁)
Given point: (2, -3) and slope: 2
y + 3 = 2(x - 2)
2. Convert to slope-intercept form (y = mx + b)
Expand: y + 3 = 2x - 4
Add -3 to both sides: y = 2x - 4 -3
Simplify: y = 2x -7
3. Convert to standard form (Ax + By + C = 0)
Start with slope-intercept: y = 2x -7
Move all terms to one side: 2x - y -7 = 0
4. Find intercepts
Y-intercept (x = 0): y = -7.0000
X-intercept (y = 0): x = 3.5000
Example Calculation
Point-Slope Form
Given: Point (2, -3) and slope = 2
Point-slope form: y - (-3) = 2(x - 2)
Simplified: y + 3 = 2(x - 2)
Slope-intercept: y = 2x - 7
Standard form: 2x - y - 7 = 0
Key Formulas
Point-Slope Form
y - y₁ = m(x - x₁)
Slope-Intercept Form
y = mx + b
Standard Form
Ax + By + C = 0
Slope Formula
m = (y₂ - y₁)/(x₂ - x₁)
Calculator Tips
Point-slope form uses any point on the line
Slope-intercept form uses the y-intercept point (0, b)
All forms represent the same line
Use point-slope when you know a point and slope
Understanding Point-Slope Form
What is Point-Slope Form?
Point-slope form is a way to write the equation of a straight line when you know the slope and any point on the line. It's particularly useful when the y-intercept is not readily available.
Key Components
- •(x₁, y₁): Coordinates of a known point on the line
- •m: The slope of the line (rise over run)
- •(x, y): Any other point on the line
Form Conversions
Point-Slope to Slope-Intercept
Start: y - y₁ = m(x - x₁)
Expand: y - y₁ = mx - mx₁
Solve for y: y = mx - mx₁ + y₁
Result: y = mx + b (where b = y₁ - mx₁)
Point-Slope to Standard
Start: y - y₁ = m(x - x₁)
Expand: y - y₁ = mx - mx₁
Rearrange: mx - y + (y₁ - mx₁) = 0
Result: Ax + By + C = 0
When to Use Point-Slope Form
Given Point & Slope
When you know the coordinates of one point and the slope of the line
Two Points Given
Calculate slope first, then use point-slope form with either point
Finding Equations
Most direct method when y-intercept is not immediately known
Real-World Applications
Physics
Linear motion, velocity-time relationships, force calculations
Economics
Cost functions, supply and demand curves, linear regression
Engineering
Stress-strain relationships, temperature gradients, rate calculations