Let the slope of line Ax + By + C = 0 be m
Ax + By + C = 0
So, y = \( -\dfrac{A}{B}x+\dfrac{C}{B}\)
m = \( -\dfrac{A}{B}\)
By using the formula,
Equation of the line passing through point (x1, y1) and having slope
m = \( -\dfrac{A}{B}\) is
y – y1 = m (x – x1)
y – y1= \( -\dfrac{A}{B}\) (x – x1)
B (y – y1) = -A (x – x1)
A(x – x1) + B(y – y1) = 0
So, the line through point (x1, y1) and parallel to the line
Ax + By + C = 0 is A (x – x1) + B (y – y1) = 0
Hence proved.
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