5.12.3: Formula Review
5.1 Algebraic Expressions
- Distributive Property: \(a(b+c)=a b+a c\)
5.3 Linear Inequalities in One Variable with Applications
- For any numbers \(a, b\), and, if \(a<b\), then \(a+c<b+c\) and \(a-c<b-c\).
- For any numbers \(a, b\), and \(c\), if \(a>b\), then \(a+c>b+c\) and \(a-c>b-c\).
- For any numbers \(a, b\), and \(c\), multiply or divide by a positive:
if \(a<b\) and \(c>0\), then \(a c<b c\) and \(\frac{a}{c}<\frac{b}{c}\) if \(a>b\) and \(c>0\), then \(a c>b c\) and \(\frac{a}{c}>\frac{b}{c}\) multiply or divide by a negative:
if \(a<b\) and \(c<0\), then \(a c>b c\) and \(\frac{a}{c}>\frac{b}{c}\)
if \(a>b\) and \(c<0\), then \(a c<b c\) and \(\frac{c}{a}<\frac{c}{c}\)
5.8 Graphing Functions
-
To calculate slope \((m)\), use the formula
\[m=\frac{r i s e}{r u n} \nonumber \]
where the rise measures the vertical change and the run measures the horizontal change.
- To find the slope of the line between two points \(\left(x_1, y_1\right)\) and \(\left(x_2, y_2\right)\), use the formula \(m=\frac{y 2-y 1}{x 2-x 1}\)