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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