Y-Intercept Calculator
Find x-intercept, y-intercept, and slope of linear equations
Calculate Line Intercepts
General Form: ax + by + c = 0
Calculation Results
Y-Intercept
X-Intercept
Slope
Step-by-Step Solution
Example Calculations
Example 1: General Form
Given: 2x + 3y - 6 = 0
Y-intercept: Set x = 0: 3y - 6 = 0 → y = 2
X-intercept: Set y = 0: 2x - 6 = 0 → x = 3
Slope: m = -a/b = -2/3 ≈ -0.667
Example 2: Slope-Intercept Form
Given: y = -2x + 4
Y-intercept: c = 4
X-intercept: Set y = 0: 0 = -2x + 4 → x = 2
Slope: m = -2
Example 3: From Intercepts
Given: x-intercept = 3, y-intercept = 2
Slope: m = -y₀/x₀ = -2/3 ≈ -0.667
Equation: y = -⅔x + 2 or 2x + 3y - 6 = 0
Key Formulas
General Form
Y-Intercept
X-Intercept
Slope
Slope-Intercept
Key Concepts
Y-Intercept: Point where line crosses y-axis
x-coordinate is always 0
X-Intercept: Point where line crosses x-axis
y-coordinate is always 0
Slope: Rate of change
Rise over run (Δy/Δx)
Vertical Line: No y-intercept
Infinite slope
Real-World Applications
Economics
Cost analysis, break-even points
Engineering
Linear relationships, trend analysis
Data Science
Linear regression, predictions
Education
Grade tracking, performance analysis
Understanding Y-Intercept and Linear Equations
What is a Y-Intercept?
The y-intercept is the point where a line crosses the y-axis. It represents the value of y when x equals zero. In many real-world scenarios, the y-intercept represents the starting value or initial condition.
Finding Intercepts
To find the y-intercept, substitute x = 0 into the equation. To find the x-intercept, substitute y = 0 into the equation. These intercepts help you quickly sketch the line and understand its behavior.
For ax + by + c = 0:
Y-intercept: y = -c/b
X-intercept: x = -c/a
Slope: m = -a/b
Different Forms of Linear Equations
General Form: ax + by + c = 0
Most comprehensive form
Slope-Intercept: y = mx + c
Directly shows slope and y-intercept
Point-Slope: y - y₁ = m(x - x₁)
Useful when you know a point and slope
Special Cases
- • Vertical lines: x = k (no y-intercept, infinite slope)
- • Horizontal lines: y = k (slope = 0, y-intercept = k)
- • Lines through origin: Both intercepts are 0