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ax + by + c = 0

ax + by + c = 0. An alternative for the equation of a straight line is given by:. This equation is used to avoid fractions. It can make the equation of a line look “tidier”. a, b & c are all integers and usually a > 0. eg 5x - 4y + 7 = 0 Note: Integers = {….-2, -1, 0, 1, 2, …..}.

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ax + by + c = 0

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  1. ax + by + c = 0 An alternative for the equation of a straight line is given by: This equation is used to avoid fractions. It can make the equation of a line look “tidier”. a, b & c are all integers and usually a > 0. eg 5x - 4y + 7 = 0 Note: Integers = {….-2, -1, 0, 1, 2, …..}

  2. Example 1: (y = mx + c ax + by + c = 0) Suppose that y = -3/5x + 2/3 X 15 We now get 15y = -9x + 10 Move all to left This becomes 9x + 15y - 10 = 0 Example 2: (ax + by + c = 0 y = mx + c) Find the gradient & intercept for 6x + 3y - 16 = 0 Starting with6x + 3y - 16 = 0 (-6x & +16) We now get 3y = -6x + 16 3 Finally we have y = -2x + 16/3 This line has gradient -2 and intercept (0, 16/3)

  3. Example 3 Prove that the line meeting the X-axis at 63.43° is parallel to 10x - 5y + 7 = 0. Line 1 m = tan  m = tan 63.43° m = 2 Line 2 10x - 5y + 7 = 0 10x + 7 = 5y y = 2x + 7/5 m=2 Lines have same gradient so must be parallel.

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