O Level MathematicsC3.5 Equations of linear graphs (interpret and obtain $y = mx + c$).

📈 Mastering Linear Equations: Decode y = mx + c!

Edudent Academy
31 Dec 25

Linear graphs pop up everywhere in O-Level exams, science experiments, and even everyday budgeting. **Understanding how to read and write the equation y=mx+cy = mx + c turns messy data into clear, predictable trends**, making this skill a must-have for any student aiming for top marks.

What Does y=mx+cy = mx + c Mean?

In the slope-intercept form, **mm represents the gradient (how steep the line is)**, while **cc is the yy-intercept (where the line cuts the yy-axis)**. If you can spot or calculate these two values, you instantly unlock the full equation of the line.

Key Takeaways & Worked Example

  • Key Idea 1: Gradient m=vertical changehorizontal changem = \frac{\text{vertical change}}{\text{horizontal change}}.
  • Key Idea 2: Intercept cc is the yy-value when x=0x = 0.
  • Problem: Find the equation of the line that passes through (2,3)(2,3) and (6,11)(6,11).
  • Step 1:
    m=11−36−2=2m = \frac{11 - 3}{6 - 2} = 2
  • Step 2: Substitute (2,3)(2,3) into y=mx+cy = mx + c:
    3=2(2)+c  ⇒  c=−13 = 2(2) + c \;\Rightarrow\; c = -1
  • Equation:
    y=2x−1\boxed{y = 2x - 1}