Linear Equation Solver
Solve linear equations in standard form: ax + b = 0
Equation: ax + b = 0
Must not be zero
Your Equation:
3x -9 = 0
Quick Examples:
Solution
Solution
x = 3.0000
Step-by-Step Solution:
1. Start: 3x -9 = 0
2. Subtract -9: 3x = 9
3. Divide by 3: x = 9 ÷ 3
4. Answer: x = 3.0000
Verification:
3 × 3.0000 -9
= 0.000000
≈ 0 ✓
Slope (m)
3
Y-intercept
-9
Formula
x = -b / a
Understanding Linear Equations
A linear equation is a first-degree polynomial equation in standard form: ax + b = 0, where a ≠ 0. It represents a straight line when graphed.
Standard Form
ax + b = 0
Where:
- a: Coefficient of x (slope when rearranged to y = mx + c)
- b: Constant term (y-intercept when rearranged)
- x: Variable to solve for
Solution Formula
x = -b / a
Example
Solve: 3x - 9 = 0
- Given: a = 3, b = -9
- Apply formula: x = -(-9) / 3
- Simplify: x = 9 / 3 = 3
- Check: 3(3) - 9 = 9 - 9 = 0 ✓
Graphical Interpretation
- Solution x represents where line crosses x-axis (y = 0)
- Slope = a (positive slopes rise, negative slopes fall)
- Y-intercept = b (where line crosses y-axis)
Applications
- Physics: Uniform motion, force calculations
- Economics: Supply and demand curves
- Business: Break-even analysis
- Engineering: Linear relationships