Straight-Line Graphs (Copy)

7 Straight-Line Graphs – Cheat Sheet

Equation of a Straight Line

• General form: y = mx + c
  • m = gradient (slope)
  • c = y-intercept
• Gradient formula: m = (y₂ – y₁) / (x₂ – x₁)
• Horizontal line: m = 0 → y = k
• Vertical line: gradient undefined → x = k
• Intercept form: x/a + y/b = 1

Parallel & Perpendicular Lines

• Parallel: m₁ = m₂
• Perpendicular: m₁ × m₂ = –1

Midpoint & Distance

• Midpoint M = ( (x₁ + x₂)/2 , (y₁ + y₂)/2 )
• Distance d = √[(x₂ – x₁)² + (y₂ – y₁)²]

Perpendicular Bisector

1. Find midpoint M.
2. Find slope m of segment.
3. Perpendicular slope = –1/m.
4. Use point-slope form y – y₁ = m(x – x₁).

Transformations to Straight-Line Form

1. Power law: y = A xⁿ
   • ln y = ln A + n ln x → plot ln y vs ln x
   • Gradient = n, Intercept = ln A
2. Exponential: y = A bˣ
   • ln y = ln A + x ln b → plot ln y vs x
   • Gradient = ln b, Intercept = ln A
3. Other forms:
   • y² = A x³ + B → plot y² vs x³
   • y³ = A ln x + B → plot y³ vs ln x

Special Cases

• Gradient from angle θ: m = tan θ
• Equation from two points:
  1. Find m
  2. Use y – y₁ = m(x – x₁)