Formulas: algebra, grade 8

The linear function

A linear function – $\displaystyle m$ the slope; the line crosses the $\displaystyle y$ -axis at $\displaystyle (0,b)$
$\displaystyle y=mx+b$
The slope of the line through $\displaystyle (x_1,y_1)$ and $\displaystyle (x_2,y_2)$
$\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$
Parallel lines have the same slope
$\displaystyle m_1=m_2$
A line through the origin – $\displaystyle {b}={0}$
$\displaystyle y=mx$
A horizontal line – the slope is 0
$\displaystyle y=b$

$\displaystyle p$ percent of $\displaystyle x$
$\displaystyle \frac{p}{100}\cdot x$
$\displaystyle s$ the distance, $\displaystyle v$ the speed, $\displaystyle t$ the time
$\displaystyle s$ $\displaystyle =$ $\displaystyle v\cdot t$

Adding or subtracting the same number on both sides – the sign stays
$\displaystyle a+c<b+c$ $\displaystyle a<b$
Multiplying or dividing by a positive number – the sign stays
$\displaystyle a\cdot c<b\cdot c$ $\displaystyle a<b,\ c>0$
Multiplying or dividing by a negative number – the sign turns round
$\displaystyle a\cdot c>b\cdot c$ $\displaystyle a<b,\ c<0$