Straight Line Graphs (Copy)
STRAIGHT LINE GRAPHS — O LEVEL & IGCSE ADDITIONAL MATHEMATICS FORMULA SHEET + COMMON MISTAKES
| Topic | Formula / Rule | Common Mistake |
|---|---|---|
| General Equation of Line | y = mx + c | Mixing gradient and intercept |
| Gradient | m = (y₂ − y₁)/(x₂ − x₁) | Reversing subtraction order |
| y-intercept | Point where x = 0 | Using y = 0 instead |
| x-intercept | Point where y = 0 | Mixing intercepts |
| Positive Gradient | Line rises left to right | Drawing downward |
| Negative Gradient | Line falls left to right | Drawing upward |
| Zero Gradient | Horizontal line | Drawing vertical line |
| Undefined Gradient | Vertical line | Saying gradient = 0 |
| Point-Slope Form | y − y₁ = m(x − x₁) | Using wrong coordinates |
| Two-Point Formula | m = (y₂ − y₁)/(x₂ − x₁) | Forgetting brackets |
| Parallel Lines | Same gradients | Thinking intercepts matter |
| Perpendicular Lines | m₁m₂ = −1 | Forgetting negative reciprocal |
| Midpoint Formula | ((x₁ + x₂)/2 , (y₁ + y₂)/2) | Dividing only one coordinate |
| Distance Formula | √[(x₂ − x₁)² + (y₂ − y₁)²] | Forgetting square root |
| Collinear Points | Same gradient between points | Using midpoint instead |
| Equation from Gradient & Point | Substitute into y − y₁ = m(x − x₁) | Forgetting rearrangement |
| Horizontal Line Equation | y = constant | Writing x = constant |
| Vertical Line Equation | x = constant | Writing y = constant |
| Gradient from Graph | Rise/run | Reversing run/rise |
| Interpreting Gradient | Rate of change | Ignoring units |
| Graph Through Origin | c = 0 | Writing non-zero intercept |
| Linear Relationship | Constant gradient | Thinking curved graph is linear |
| Direct Proportion | y = kx | Forgetting passes through origin |
| Gradient of Parallel Lines | Equal gradients | Different signs |
| Gradient of Perpendicular Lines | Negative reciprocals | Using reciprocal only |
| Equation Rearrangement | Rearrange into y = mx + c | Leaving in unsimplified form |
| Simultaneous Graphs | Intersection = solution | Giving one coordinate only |
| Graph Scale | Equal intervals | Uneven scaling |
| Coordinates | (x, y) | Reversing order |
| Linear Inequality | Shade correct region | Shading wrong side |
| Boundary Line | Solid if ≤ or ≥ | Dashed instead |
| Strict Inequality | Dashed boundary | Drawing solid line |
| Region Solution | Common shaded area | Shading entire graph |
| Gradient Interpretation | Steeper line = larger gradient | Confusing sign and steepness |
| Average Gradient | Δy/Δx | Using single point |
| Equation from Two Points | Find gradient first | Guessing equation |
| Conversion to Standard Form | Rearrange carefully | Sign mistakes |
| Graphing from Table | Plot accurately | Uneven plotting |
| Intercepts Method | Find x and y intercepts | Mixing substitutions |
Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total A Grades, 11 World Records and 7 Distinctions, Educate A Change.
QUICK STRAIGHT LINE FORMULAS
| Formula | Expression |
|---|---|
| General Equation | y = mx + c |
| Gradient Formula | m = (y₂ − y₁)/(x₂ − x₁) |
| Point-Slope Form | y − y₁ = m(x − x₁) |
| Midpoint Formula | ((x₁ + x₂)/2 , (y₂ + y₁)/2) |
| Distance Formula | √[(x₂ − x₁)² + (y₂ − y₁)²] |
QUICK GRADIENT RULES
| Situation | Result |
|---|---|
| Positive Gradient | Rising line |
| Negative Gradient | Falling line |
| Zero Gradient | Horizontal line |
| Undefined Gradient | Vertical line |
| Parallel Lines | Same gradient |
| Perpendicular Lines | Product = −1 |
Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total A Grades, 11 World Records and 7 Distinctions, Educate A Change.
QUICK LINE EQUATIONS TABLE
| Line Type | Equation |
|---|---|
| Horizontal Line | y = a |
| Vertical Line | x = a |
| Through Origin | y = mx |
| Direct Proportion | y = kx |
QUICK GRAPH RULES
| Situation | Rule |
|---|---|
| y-intercept | Put x = 0 |
| x-intercept | Put y = 0 |
| Steeper Line | Larger magnitude gradient |
| Straight Line | Constant rate of change |
| Intersection Point | Solve simultaneously |
LINEAR INEQUALITIES RULES
| Inequality | Boundary |
|---|---|
| y < mx + c | Dashed line |
| y > mx + c | Dashed line |
| y ≤ mx + c | Solid line |
| y ≥ mx + c | Solid line |
Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total A Grades, 11 World Records and 7 Distinctions, Educate A Change.
EXAM HACKS
| Situation | Fast Trick |
|---|---|
| Find equation quickly | Use y = mx + c |
| Two-point question | Find gradient first |
| Parallel line | Copy gradient |
| Perpendicular line | Flip and change sign |
| Graph sketch | Plot intercepts first |
| Linear inequality | Test point method |
| Direct proportion | Graph passes through origin |
| Vertical line | x = constant |
MOST COMMON LOSSES OF MARKS
| Mistake | Why Marks Are Lost |
|---|---|
| Reversing gradient formula | Wrong gradient |
| Mixing x and y intercepts | Incorrect graph |
| Wrong perpendicular gradient | Entire equation wrong |
| Sign mistakes in rearranging | Wrong final equation |
| Uneven graph scale | Plotting errors |
| Incorrect shading | Wrong inequality region |
| Dashed vs solid confusion | Boundary marks lost |
| Coordinate reversal | Incorrect points |
| Missing units in interpretation | Context marks lost |
| Poor graph plotting | Accuracy marks lost |
Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total A Grades, 11 World Records and 7 Distinctions, Educate A Change.