Contemporary Mathematics

# Formula Review

## 5.1Algebraic Expressions

• Distributive Property: $a(b+c)=ab+aca(b+c)=ab+ac$

## 5.3Linear Inequalities in One Variable with Applications

• For any numbers $aa$, $bb$, and $,,$ if $a, then $a+c and $a−c.
• For any numbers $aa$, $bb$, and $cc$, if $a>ba>b$, then $a+c>b+ca+c>b+c$ and $a−c>b−ca−c>b−c$.
• For any numbers $aa$, $bb$, and $cc$,
multiply or divide by a positive:
if $a and $c>0c>0$, then $ac and $ac
if $a>ba>b$ and $c>0c>0$, then $ac>bcac>bc$ and $ac>bcac>bc$
multiply or divide by a negative:
if $a and $c<0c<0$, then $ac>bcac>bc$ and $ac>bcac>bc$
if $a>ba>b$ and $c<0c<0$, then $ac and $ac

## 5.8Graphing Functions

• To calculate slope $(m)(m)$, use the formula
$m=riserunm=riserun$,
where the rise measures the vertical change and the run measures the horizontal change.
• To find the slope of the line between two points $(x1,y1)(x1,y1)$ and $(x2,y2)(x2,y2)$, use the formula
$m=y2−y1x2−x1m=y2−y1x2−x1$
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