📚 Key Concepts
Slope (gradient) of a lineDifferent forms of line equation:- Point-slope form
- Slope-intercept form
- Two-point form
- Intercept form
Angle between linesParallel and perpendicular linesDistance of point from lineFamily of lines
🎯 Key Formulas
Slope (m) = (y₂-y₁)/(x₂-x₁)Point-slope form: y - y₁ = m(x - x₁)Slope-intercept form: y = mx + cTwo-point form: (y-y₁)/(y₂-y₁) = (x-x₁)/(x₂-x₁)Intercept form: (x/a) + (y/b) = 1Distance formula: |ax₁ + by₁ + c|/√(a² + b²)Angle between lines: tan θ = |m₁-m₂|/(1+m₁m₂)Parallel lines: m₁ = m₂Perpendicular lines: m₁m₂ = -1
⚠️ Common Mistakes to Avoid
Wrong slope calculationIncorrect sign in distance formulaConfusion between different formsWrong angle calculationMisidentifying parallel/perpendicular linesIncorrect y-intercept identification
📖 Knowledge Prerequisites
Coordinate geometry basicsBasic algebraTrigonometry fundamentalsDistance concepts
💡 Tips for Students
Always check slope signVerify parallel/perpendicular conditionsDraw diagrams for visualizationRemember intercept formula signsPractice converting between forms
👉 Practice Recommedations
Calculate slopesFind equations of linesDetermine angles between linesFind distances from pointsWork with parallel linesPractice with perpendicular linesSolve word problems
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