Overview
This lecture explains why linear equations are commonly written in the form y = mx + c, clarifies the meaning of m (gradient) and c (y-intercept), and demonstrates how to rearrange equations into this standard form for graphing.
Standard Form of Linear Equations
- Linear equations are usually written as y = mx + c for convenience and easy comparison.
- This standardization makes it simple to visualize and sketch lines on a graph.
Components of y = mx + c
- m represents the gradient, indicating the steepness of the line.
- c represents the y-intercept, marking where the line crosses the y-axis.
Example: Identifying m and c
- In y = 2x + 3, m = 2 (gradient) and c = 3 (y-intercept).
- The line crosses the y-axis at y = 3 and rises 2 units for every 1 unit it moves horizontally.
Rearranging to Standard Form
- If an equation is not in y = mx + c form, rearrange it to identify m and c easily.
- Example: 2y - 4x = 6 → 2y = 4x + 6 → y = 2x + 3.
Additional Example
- For 4y + 16 = 2x, rearrange: 4y = 2x - 16 → y = 0.5x - 4.
- Here, m = 0.5 and c = -4.
Equations With Missing Terms
- If no c value: treat as c = 0, so the line crosses y-axis at 0.
- If no m value: m = 1 is implied.
- Always identify m and c for graphing.
Key Terms & Definitions
- Gradient (m) — The slope showing how steep a line is; rise over run.
- Y-intercept (c) — The value where the line crosses the y-axis.
Action Items / Next Steps
- Practice rearranging equations into y = mx + c form.
- Sketch lines using identified m and c values.