Drawing Linear Graphs

3.2 Drawing Linear Graphs – Cheat Sheet

1. Linear Graph Basics

• Linear equation: y = mx + c or in general form ax + by = d
• m = gradient (slope)
• c = y-intercept (point where line crosses y-axis)
• Graph is always a straight line

2. Steps to Draw a Linear Graph

1. If in form y = mx + c:
   • c = y-intercept → plot (0, c)
   • m = gradient = rise/run → move from y-intercept using slope
2. If in form ax + by = d:
   • Find y-intercept (x = 0)
   • Find x-intercept (y = 0)
   • Join these points with a straight line
3. Extend line across graph and label it

3. Gradient (m) Interpretation

• Positive m → line rises from left to right
• Negative m → line falls from left to right
• m = 0 → horizontal line
• Undefined slope → vertical line (x = constant)

4. Worked Examples

Example 1: y = −2x + 5

• y-intercept: (0, 5)
• Gradient = −2 → down 2, right 1 from intercept
• Second point: (1, 3) → draw line through (0, 5) and (1, 3)

Example 2: y = 7 − 4x

• Rewrite: y = −4x + 7
• y-intercept: (0, 7)
• Gradient = −4 → down 4, right 1
• Second point: (1, 3)

Example 3: 3x + 2y = 5

• For y-intercept: x = 0 → 2y = 5 → y = 2.5 → (0, 2.5)
• For x-intercept: y = 0 → 3x = 5 → x = 5/3 → (5/3, 0)
• Draw line through these points

5. Quick Graph Plot Table