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Equations of a Straight Line

An equation that represents a straight line in mathematical form is called an equation of a straight line.

A straight line can be expressed in mathematical form algebraically. There are five ways to write straight lines in algebraic form mathematically. Learn all of them one after one to understand the different cases of expressing straight lines in mathematics.

Slope Intercept form

There are two types of slope intercept form linear equations. The first one is slope x-intercept form and the second one is slope y-intercept form of straight line.

$(1) \,\,\,\,\,\,$ $y \,=\, mx+c$

$(2) \,\,\,\,\,\,$ $x \,=\, m’y+c$

Line passes through Origin with slope

A linear equation in algebraic form when the straight line passes through origin with slope in two dimensional space.

$y \,=\, mx$

Intercept form

A linear equation in algebraic form in terms of $x$ and $y$ intercepts.

$\dfrac{x}{a}+\dfrac{y}{b} \,=\, 1$

Point Slope form

A linear equation in algebraic form in terms of coordinates of a point and slope.

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

Two Point form

A linear equation in algebraic form in terms of coordinates of two points.

$y-y_{1} \,=\, \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}(x-x_{1})$

Standard form

The above five cases of linear equations are simply written generally in the following standard form linear equation.

$ax+by+c \,=\, 0$