# Fundamental Mathematics/Arithmetic/Arithmetic Equation/Linear Equation

## Linear equation

${\displaystyle f(x)=ax+b=0}$

In this equation,

f(x) represents function
x represents the x axis
b represents the y-intercept.

## Finding equation's root

To find value satisfy linear equation above by dividing both sides by a

${\displaystyle x+{\frac {b}{a}}=0}$
${\displaystyle x=-{\frac {b}{a}}}$

Hence, x is the root of equation

## Straight line

${\displaystyle y=ax+b}$

Gradient is worked out by :${\displaystyle rise/run\,}$ , rise being the distance a line travels vertically, and run being the distance it travels horizontally. The y-intercept (or y-int) is the point on a linear graph where a linear equation crosses the y-axis. Similarly, the x-intercept (or x-int) is the point where a linear equation crosses the x-axis.

for x=0

${\displaystyle y=a(0)+b\ =b}$ indicates y-intercept

for y=0

${\displaystyle 0=ax+b}$ indicates x-intercept
${\displaystyle x=-{\frac {b}{a}}}$

For every value of x there is a corresponding value as shown below

 x 0 1 2 y b a+b 2a+b