Equations of Linear Graph (Copy)

Equation of a Straight Line Cheat Sheet (IGCSE Mathematics 0580 – CORE)
Topic: Interpreting and Finding y = mx + c

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. Identifying m and c from an Equation

• Gradient (m): Coefficient of x
• Y-Intercept (c): Constant term

Example:
Equation: y = 6x + 3

• Gradient = 6
• y-Intercept = 3

3. Finding the Equation of a Line Given a Graph

Steps:

1. Find the gradient (m):
   • Use two points on the line.
   • Gradient = (change in y) ÷ (change in x) = rise ÷ run
2. Find the y-intercept (c):
   • Find where the line crosses the y-axis (where x = 0).
3. Write the equation in the form y = mx + c.

4. Special Case: Vertical Line

• Equation of a vertical line: x = k
  • k is a constant value.
  • Line is parallel to the y-axis.
  • No gradient is defined (slope is undefined).

Example:
Line passes through x = 2 → Equation: x = 2

5. Example Problems

• Given graph passes through (0, 2) and (3, 5):
  • Gradient = (5 – 2)/(3 – 0) = 3/3 = 1
  • y-Intercept = 2
  • Equation: y = x + 2
• Given equation y = –2x + 5:
  • Gradient = –2
  • y-Intercept = 5
• Vertical line through x = –4:
  • Equation: x = –4

6. Important Notes

• Always simplify the equation fully (no fractions left if possible).
• Check by substituting points back into your equation to verify.
• If given two points, use them to find gradient first, then use one point to find c.

Summary Table

CORE-level exams expect clear identification of gradient and intercept, finding full equations from graphs or points, and simple interpretation tasks without needing advanced methods like perpendicular or parallel lines unless specified.