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Prove that the line through the point (x1, y1) and parallel to the line Ax + By + C = 0 is A (x –x1) + B (y – y1) = 0.

Q : 11        Prove that the line through the point  (x_1,y_1)  and parallel to the line   Ax+By+C=0   is   A(x-x_1)+B(y-y_1)=0.

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It is given that line is parallel to the line  Ax+By+C=0
Therefore, their slopes are equal
The slope of line Ax+By+C=0  , m'= \frac{-A}{B}
Let the slope of other line be m
Then,
m =m'= \frac{-A}{B}
Now, the equation of the line passing through the point (x_1,y_1)  and with slope -\frac{A}{B}  is
(y-y_1)= -\frac{A}{B}(x-x_1)
B(y-y_1)= -A(x-x_1)
A(x-x_1)+B(y-y_1)= 0
Hence proved 

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