# Algebra Homework Help Formula Definition

## Using the Slope Formula

Do you have trouble remembering all of the algebra formulas, especially the slope formula? If so, you're in luck! Here you'll find a quick reference sheet with all of the formulas for slope.

Let's start by identifying slope.

## Definition of Slope

The slope of a line defines the steepness of the line and whether the line rises or falls.

The definition of slope is the **rise divided by the run**, written as:

The slope is calculated by counting the rise and then counting the run. We then write the slope as a fraction.

We use this definition when calculating slope or graphing slope.

Graphing slope also leads us to a very popular method for graphing linear equations, slope intercept form.

## Slope Intercept Form

When a linear equation is written in slope intercept form, the slope of the line can easily be identified. The slope is "m" or the coefficient of x in the equation.

Often times a graph is not present, and we must calculate the slope when given two ordered pairs. In this case we must use another special formula.

## Calculating Slope Given Two Points

When given two points, the following formula can be used to determine the slope of the line:

This formula is commonly used to solve rate of change problems. Click here for detailed examples on using this formula.

Keeping a reference sheet of formulas is a great way to study Algebra. Slope is a very important concept to remember in Algebra, so make sure you add these formulas and definitions to your reference sheet or study guide.

## Common Algebra Formulas

Here are some of the most commonly used formulas in algebra. If you have one you'd like to be added, or find an error, please contact me.

## Laws of Exponents

- \(a^ma^n=a^{m+n}\)
- \((a*b)^m=a^mb^m\)
- \((a^m)^n=a^{mn}\)
- \(a^{\frac{m}{n}}=\sqrt[n]{a^m}\)
- \(a^0=1\)
- \(\frac{a^m}{a^n}=a^{m-n}\)
- \(a^{-m}=\frac{1}{a^m}\)

## Quadratic Formula

For an equation of the form \(ax^2+bx+c=0\), you can solve for x using the Quadratic Formula:

$$ x = \frac{-b \pm \sqrt{b^2-4ac}}{2a} $$## Binomial Theorem

- \((a+b)^1= a + b\)
- \((a+b)^2=a^2+2ab+b^2\)
- \((a+b)^3=a^3+3a^2b+3ab^2+b^3\)
- \((a+b)^4=a^4+4a^3b+6a^2b^2+4ab^3+b^4\)

## Difference of Squares

## Rules of Zero

- \(\frac{0}{x} = 0\text{, where }x \neq 0.\)
- \(a^0=1\)
- \(0^a=0\)
- \(a*0 = 0\)
- \(\frac{a}{0}\text{ is undefined (you can't do it)}\)

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