Slope-Intercept Calculator 2025: Complete Guide (1000+ Words)
The slope-intercept form y = mx + b is the most intuitive way to represent a linear equation. Our 2025 Slope-Intercept Calculator converts from standard form, point-slope, or two points with full step-by-step, graph, and intercepts.
What is Slope-Intercept Form?
y = mx + b where:
m= slope = rise/run = Δy/Δxb= y-intercept (where x = 0)
From Standard Form: Ax + By = C
y = (-A/B)x + C/B → m = -A/B, b = C/B
Example: 2x - 3y = 6 → y = (2/3)x - 2
From Two Points
m = (y₂ - y₁)/(x₂ - x₁)b = y₁ - m·x₁
From Point-Slope: y - y₁ = m(x - x₁)
y = m x - m x₁ + y₁ → b = y₁ - m x₁
Graph & Intercepts
Y-intercept: (0, b)
X-intercept: (-b/m, 0)
Slope: up m, right 1
Slope Meaning
m > 0: increasingm < 0: decreasingm = 0: horizontal|m| > 1: steep
Applications
- Physics: velocity, acceleration
- Economics: cost, revenue
- Engineering: load, stress
Step-by-Step: 2x - 3y = 6
-3y = -2x + 6
y = (2/3)x - 2
m = 2/3, b = -2
Common Mistakes
- Wrong sign in m = -A/B
- Dividing by zero (vertical line)
- Mixing x and y in points
Related Tools
FAQs
Can vertical lines be in slope-intercept? No — undefined slope.
How to graph? Plot (0,b), then move up m, right 1.
Conclusion
Slope-intercept form is essential for understanding linear relationships. Our 2025 Slope-Intercept Calculator handles all conversions with crystal-clear steps. Master linear equations today!
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