Equation of a Straight Line — Part 1: Slope, inclination and the forms of a line: visual lesson, ICSE Class 10 Mathematics

Lesson

Equation of a Straight Line, Part 1

Every straight line on a graph has an equation in $x$ and $y$ . Its slope tells how steep it is; its intercepts tell where it crosses the axes.

In this lesson you will

Find the inclination and slope of a line, using m = tan θ
Calculate the slope of the line through two points and test points for collinearity
Write and read the slope-intercept form y = mx + c
Find the equation of a line from a point and a slope, or from two points

$y = \dfrac{1}{2}x + 1$

One line, one equation: $y = \dfrac{1}{2}x + 1$.

Concept

What you will be able to do

Find the inclination and slope of a line
Calculate the slope from two points, and test points for collinearity
Write and read $y = mx + c$
Find the equation from a point and a slope, or from two points

Concept

Inclination and slope

The inclination $\theta$ of a line is the angle it makes with the positive direction of the $x$ -axis, measured anticlockwise ( $0^\circ \le \theta < 180^\circ$ ). Its slope (gradient) is

m = \tan \theta

The slope is the tangent of the inclination.
Inclination $\theta$	Slope $m = \tan \theta$	The line is
$0^\circ$	$0$	horizontal
$30^\circ$	$\dfrac{1}{\sqrt{3}}$	rising gently
$45^\circ$	$1$	rising, at equal steps
$60^\circ$	$\sqrt{3}$	rising steeply
$90^\circ$	not defined	vertical
$135^\circ$	$-1$	falling

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