Math Doubts

Slope of a Straight Line in coordinates form

Equation

$m \,=\, \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$

The ratio between differences of ordinates and abscissae of any two points on a line is called slope of a straight line.

Introduction

$\overleftrightarrow{PQ}$ is a straight line with some inclination in Cartesian coordinate system.

slope of straight line in coordinates

The coordinates of $P$ and $Q$ are $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$. Draw a parallel line to horizontal axis from point $P$ and also draw a perpendicular line to same axis from point $Q$. The two lines are intersected at point $R$.

The length of $\overline{QR}$ represents vertical rise of the points $P$ and $Q$ and the length of $\overline{PR}$ represents the horizontal distance between them. The ration between them is called gradient of the straight line and it is denoted by letter $m$.

$m \,=\, \dfrac{Vertical \, Rise}{Horizontal \, Distance}$

$\implies m \,=\, \dfrac{QR}{PR}$

$\implies m \,=\, \dfrac{OQ-OR}{OR-OP}$

$\,\,\, \therefore \,\,\,\,\,\, m \,=\, \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$

In this example, $x_{1}$ and $x_{2}$ are called abscissae and $y_{1}$ and $y_{2}$ are called ordinates geometrically.

It is proved that the slope of a straight line in terms of a coordinates is the ratio of differences of ordinates and abscissae of any two points on a line.

Math Doubts

A best free mathematics education website that helps students, teachers and researchers.

Maths Topics

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

Maths Problems

A math help place with list of solved problems with answers and worksheets on every concept for your practice.

Learn solutions

Subscribe us

You can get the latest updates from us by following to our official page of Math Doubts in one of your favourite social media sites.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved