A line passes through (x₁, y₁) and (h, k). If slope of the line is m, show that k-y₁=m(h-x₁)

Question

A line passing through the point \( A(9, 0) \) makes an angle of \( 30^\circ \) with the positive direction of the x-axis. If this line is rotated about \( A \) through an angle of \( 15^\circ \) in the clockwise direction, then its equation in the new position is:

Answer 1

Given:

A straight line passes through the points:
(x₁, y₁) and (h, k)

Slope of the line = m

Step 1: Write the formula for slope

The slope of a line passing through two points (x₁, y₁) and (h, k) is:

m = (k − y₁) / (h − x₁)

Step 2: Rearrange the equation

Multiply both sides by (h − x₁):

k − y₁ = m (h − x₁)

Final Result:

Hence, it is proved that:
k − y₁ = m (h − x₁)

A line passes through (x₁, y₁) and (h, k). If slope of the line is m, show that k-y₁=m(h-x₁)

Solution and Explanation

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A line passes through (x₁, y₁) and (h, k). If slope of the line is m, show that k-y₁=m(h-x₁)