Drawing Linear Graph (Copy)
Drawing Straight-Line Graphs Cheat Sheet (IGCSE Mathematics 0580 – CORE)
Topic: Linear Graphs (y = mx + c Form)
1. Standard Form of a Straight Line
- y = mx + c
Where:
- m = gradient (slope)
- c = y-intercept (where the line crosses the y-axis)
2. Understanding the Parts
- Gradient (m):
- Positive m → Line slopes upwards from left to right
- Negative m → Line slopes downwards from left to right
- m = 0 → Horizontal line (flat)
- Y-Intercept (c):
- The value of y when x = 0
- Point where the line crosses the y-axis
3. Steps to Draw a Straight-Line Graph
- Identify the y-intercept (c).
- Plot the point (0, c) on the graph.
- Use the gradient (m) to find another point:
- Gradient = “rise over run” →
- Rise = change in y (up or down)
- Run = change in x (always right)
Example:
- m = 2 → up 2 units, right 1 unit
- m = –3 → down 3 units, right 1 unit
- Gradient = “rise over run” →
- Draw a straight line through the points using a ruler.
4. Example
Equation: y = –2x + 5
- Y-intercept (c) = 5 → Point (0, 5)
- Gradient (m) = –2 →
- Means: Down 2, right 1
Steps:
- Start at (0, 5)
- Move down 2, right 1 → second point (1, 3)
- Connect the points with a ruler.
5. Special Cases
- y = constant (e.g., y = 4)
→ Horizontal line through y = 4 - x = constant (e.g., x = –2)
→ Vertical line through x = –2
(Only in special cases; x = constant is not y = mx + c form)
6. Table of Values Method (if given)
- Substitute several x-values (usually –2, –1, 0, 1, 2) into the equation
- Find corresponding y-values
- Plot the (x, y) points
- Join with a straight line
Example: y = x – 1
| x | –2 | –1 | 0 | 1 | 2 |
|---|---|---|---|---|---|
| y | –3 | –2 | –1 | 0 | 1 |
Plot these points and draw the line.
7. Key Reminders
- Use a ruler for all straight lines.
- Always extend the line beyond the plotted points.
- Label the line with its equation if needed.
- Check two points are enough for a straight line.
- Read scales carefully if graph paper is used.
This method is CORE-level and is mainly about simple straight-line plotting, not finding intersections or complex graph interpretation.