# 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

**Solution:**

The slope of line Ax + By + C = 0 or y = (- A/B)x + (- C/B) is m = - A/B

It is known that parallel lines have the same slope.

Therefore, slope of the other line = m = - A/B

The equation of the line passing through point (x_{1}, y_{1}) and having slope m = - A/B is

y - y_{1} = m (x - x_{1})

y - y_{1} = - A/B (x - x_{1})

B (y - y_{1} = - A(x - x_{1})

A(x - x_{1}) + B (y - y_{1}) = 0

Hence, 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

NCERT Solutions Class 11 Maths Chapter 10 Exercise 10.3 Question 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

**Summary:**

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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