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Find the equation of the line passing through the given point and parallel to the given line.(3, 2); x +2y = 5?
x + 2y = 5
2y = -x + 5
y = -x/2 + 5/2
The gradient of the given line is '-1/2' ; the coefficient of 'x'.
For parallel lines the gradient is the same at '-1/2'
Hence substituting
y - 2 = ( -x -3) / 2 + 5/2
Notice you displace the given point against the corresponding (x,y)
Hence
y - 2 = -x/2 - 3/2 + 5/2
y - 2 = -x/2 + 2/2
y = -x/2 + 2 + 2/2 NB 2/2 = 1
y = -x/2 + 3
Multiplying through by '2'
2y = -x + 6
In the original form it is
x + 2y = 6 is the parallel line.
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