$x \,=\, m’y+c$

It is an equation of a straight line when a straight line intercepts $x$-axis at a point with some slope.

A straight line intercepts the horizontal $x$-axis at point $A$ with an intercept $c$ and it makes an angle of $\theta$ with horizontal axis. The point $A$ in the form of coordinates is $A(c, 0)$.

$P$ is any point on the straight line and it is $x$ and $y$ units distance from origin in horizontal and vertical axes directions respectively. So, the point $P$ in the form of coordinates is $P(x, y)$.

Therefore, the straight line is represented as $\small \overleftrightarrow{AP}$ geometrically in mathematics.

Assume, the slope of straight line is denoted by $m$ and express it in trigonometric form.

$m \,=\, \tan{\theta}$

Now, draw a perpendicular line to horizontal $x$-axis from point $P$ and it intersects the $x$-axis at point $Q$. Thus, a right triangle ($\Delta QAP$) is formed geometrically.

Calculate the $\tan{\theta}$ in trigonometric system and it is equal to the slope of the straight line.

$\tan{\theta} \,=\, \dfrac{PQ}{AQ}$

$\implies \tan{\theta} \,=\, \dfrac{PQ}{OQ-OA}$

$\implies \tan{\theta} \,=\, \dfrac{y}{x-c}$

$\implies m \,=\, \dfrac{y}{x-c}$

$\implies x-c \,=\, \dfrac{y}{m}$

$\implies x \,=\, \dfrac{y}{m}+c$

$\,\,\, \therefore \,\,\,\,\,\, x \,=\, \Big(\dfrac{1}{m}\Big)y+c$

It is a linear equation which represents an equation of a straight line when a straight line intercepts $x$-axis with an $x$-intercept and slope. Hence, it is called slope and $x$-intercept form equation of a straight line.

Take the reciprocal of $m$ as $m’$.

$\,\,\, \therefore \,\,\,\,\,\, x \,=\, m’y+c$

Latest Math Topics

Aug 31, 2024

Aug 07, 2024

Jul 24, 2024

Dec 13, 2023

Latest Math Problems

Oct 22, 2024

Oct 17, 2024

Sep 04, 2024

Jan 30, 2024

Oct 15, 2023

Copyright © 2012 - 2023 Math Doubts, All Rights Reserved