We know that there are infinite points in the coordinate plane. Consider an arbitrary point \(P(x,y)\)

Equation of a straight line contains terms in \(x\)

Different forms of equations of a straight line are discussed below.

**1. Equations of horizontal and vertical lines**

Equation of the lines which are horizontal or parallel to the \(X\)

Similarly, equation of a straight line which is vertical or parallel to \(Y\)

For example, equation of the line which is parallel to \(X\)

Similarly, equation of the line which is parallel to \(Y\)

**2. Point-slope form equation of line**

Consider a non-vertical line \(L\)

Slope of the line by the definition is,

\(m\)

\(y~-~y_1\)

For example, equation of the straight line having a slope \(m\)

\(y~-~3\)

\(y\)

\(2x~-~y~-~1\)

**3. Two-point form equation of line**

Let \(P(x,y)\)

Since the three points are collinear,

\(slope ~of ~PA\)

\(\frac{y~-~y_1}{x~-~x_1}\)

\(y – y_{1} = (y_{2} – y_{1}). \frac{x – x_{1} }{x_{2} – x_{1}}\)

**4. Slope-intercept form equation of line**

Consider a line whose slope is \(m\)

Then, equation of the line will be

\(y~-~a\)

\(y\)

Similarly, \(a\)

Equation of the line will be,

\(y\)

**5. Intercept form**

Consider a line \(L\)

By two-point form equation,

\(y~-~0\)

\(y\)

\(y\)

\(\frac{x}{a} ~+ ~\frac{y}{b} \)

For example, equation of the line which has \(x\)

\(\frac{x}{3} ~+ ~\frac{y}{4}\)

\(4x~ + ~3y\)

**6. Normal form**

Consider a perpendicular from the origin having length \(l\)

Let \(OP\)

Then,

\(OQ\)

\(PQ\)

Coordinates of the point \(P\)

slope of the line \(OP\)

Therefore,

\(Slope~ of ~the ~line ~L\)

Equation of the line \(L\)

\(y~-~l~ sin~β\)

\(y ~sin~β~-~l~ sin^2~ β\)

\(x~ cos~β~ + ~y ~sin~β\)

\(x ~cos~β~ + ~y ~sin~β\)

You have learnt about the different forms of equation of a straight line. To know more about straight lines and its properties, log onto www.byjus.com.’

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