# 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 (xo,yo) , (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)