# Ax + by + c = 0 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.

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ax + by + c = 0 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, …..} An alternative for the equation of a straight line is given by:

Example 1:(y = mx + cax + by + c = 0) Suppose that y = - 3 / 5 x + 2 / 3 Example 2:(ax + by + c = 0y = mx + c) X 15 We now get15y = -9x + 10 Move all to left This becomes9x + 15y - 10 = 0 Find the gradient & intercept for 6x + 3y - 16 = 0 Starting with 6x + 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 )

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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