Arithmetic Course/Linear Function

Linear Function

Linear Function is a function of a Straight Line

General Form

Straight Line goes through point (0,0)

For every x there is y = x

x | y

-2 | -2

-1 | -1

0 | 0

1 | 1

2 | 2

If f(x) = y Then f(x) represents a Straight Line through point (0,0) with Slope equals 1

Straight Line goes through two points

If there is a Straight Line goes through 2 points (x_o,y_o) , (x,y)

$m={\frac {y-y_{o}}{x-x_{o}}}$

$y=y_{o}+m(x-x_{o})$

Straight Line goes through Two Intercept Points

${\frac {x}{a}}+{\frac {y}{b}}=1$

When

x = 0 y = b

y = 0 x = a

Function $f(x,y)={\frac {x}{a}}+{\frac {y}{b}}=1$ of a Straight Line that cuts the x axis at (0,a) and the y axis at (0,b)