Equation of a line passing through point A(x1, y1) and having slope m�

1.	Equation of a line passing through point A(x1, y1) and having slope m (see Fig.) is y - y1 = m(x - x1)
Answer» Suppose P(x, y) is any point on the given line. Then, the slope of the line is y - y₁/x - x₁ = m Therefore, y - y₁ = m(x - x₁) Conversely, let Q(x', y') be a point such that y' - y₁ = m(x - x₁) y' - y₁/x - x₁ = m (slope of the line) This implies that the line (bar)AQ coincides with the given line which, in turn, implies that Q lies on the given line. Therefore, equation of the line is y - y₁ = m(x - x₁).

Equation of a line passing through point A(x1, y1) and having slope m (see Fig.) is y - y1 = m(x - x1)

Answer»

Suppose P(x, y) is any point on the given line. Then, the slope of the line is y - y₁/x - x₁ = m

Therefore,

y - y₁ = m(x - x₁)

Conversely, let Q(x', y') be a point such that

y' - y₁ = m(x - x₁)

y' - y₁/x - x₁ = m (slope of the line)

This implies that the line (bar)AQ coincides with the given line which, in turn, implies that Q lies on the given line. Therefore, equation of the line is y - y₁ = m(x - x₁).

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Equation of a line passing through point A(x1, y1) and having slope m (see Fig.) is y - y1 = m(x - x1)

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