Overview
This lecture explains how to determine the equation of a straight line from its graph using the general linear form y = mx + c, focusing on finding the gradient (m) and y-intercept (c).
Equation of a Straight Line
- The standard form for a straight line is y = mx + c.
- "m" represents the gradient (slope) which shows how steep the line is.
- "c" is the y-intercept, the point where the line crosses the y-axis.
Finding the Y-Intercept (c)
- The y-intercept is found where the line crosses the y-axis.
- Example: If the line crosses at y = 2, then c = 2.
- For a different example, if it crosses at y = -3, then c = -3.
Finding the Gradient (m)
- The gradient is calculated by change in y divided by change in x (Δy/Δx).
- Choose any two points on the line and label them.
- Draw a right-angled triangle between the points to visualize changes.
- Calculate change in y: subtract the y-values of the two points.
- Calculate change in x: subtract the x-values of the two points.
- Example: Δy = -9, Δx = 3, so m = -9/3 = -3.
- Another example: Δy = 1, Δx = 4, so m = 1/4.
Writing the Final Equation
- Substitute m and c into y = mx + c.
- Example: m = -3, c = 2, so equation is y = -3x + 2.
- Example: m = 1/4, c = -3, so equation is y = (1/4)x - 3.
Key Terms & Definitions
- Gradient (m) — The slope of the line, found by dividing change in y by change in x.
- Y-intercept (c) — The value where the line crosses the y-axis.
Action Items / Next Steps
- Practice finding gradients and y-intercepts from several graph examples.
- Write equations for different lines using the y = mx + c format.