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Line Equations and Gradient Calculation Examples

Learn how to find equations of lines, calculate line lengths, and determine gradients in these practical examples with step-by-step explanations. Understand concepts like y-intercept, perpendicular lines, and midpoints. Solve geometry problems easily.

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Line Equations and Gradient Calculation Examples

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  1. y-intercept = 3 So c = 3 Example 1 By examination of the graph, state the equation of the line in the formy = mx+ c - 6 3 y = -2x + 3

  2. Example 2 Calculate the length of the line from C(-4,12) to D (7.-3)

  3. Example 5 Write down the gradient of the lines perpendicular to the given line

  4. Example 6 PQ makes an angle of 32º with the positive direction of the x-axis. RS is perpendicular to PQ. Find the gradient of RS.

  5. Example 7 • T(-6,3), U(1,4), and V(-5,-4) are the vertices of triangle TUV. • M is the mid-point of UV. • Calculate mVU and mTM • (b) Explain why triangle TUV is isosceles. M (-2,0)

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