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Equation of Strait Line

I. Slope Intercept Form.

Let l is line making angle with x-axis and cutting intercept OQ = c from y-axis Let P(x, y) be any point on l.

The co-ordinates of Q is (0, c)

This is the required equation of a straight line in terms of its slope and intercept ‘c’ on the y-axis.

Note – When a straight line passes through the origin, c = 0 and the equation of line is y = mx.

II. Point slope form

Let P(x, y,) be a point on l making angle with x-axis, and cutting an intercept c on y-axis.

The equation of the line l is given by

y = mx + c ---------- (i)        [m = tan ]

Since (x₁, y₁,) lie on l

Subtracting (ii) from (i) we get y – y₁ = m(x – x₁) Which is equation of line l passing through a fixed point (x₁, y₁)

III. Two Point Form :

Let l be a line which passes through two given points P(x₁, y₁) and Q(x₂, y₂).Let m be its slope.

Then the equation of line through P(x₁, y₁) is

y – y₁ = m(x – x₁) ------- (i)

Point Q also live on it

dividing (i) by (ii) we get

This is required equation of line l passing through (x₁, y₁) and (x₂, y₂)