# Algebra Basics

## 1. Foundations

The primary purpose of the Foundations of Algebra course is to provide a basis for curriculum development for rising 9th grade students in need of substantial support prior to taking Algebra I.

## 2. Algebraic expressions

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

## 3. Linear equations and inequalities

A linear equation in one variable is an equation in which there is only one variable present. It is of the form Ax + B = 0, where A and B are any two real numbers and x is an unknown variable that has only one solution. For example, 9x + 78 = 18 is a linear equation in one variable.

## 4. Graphing lines and slope

A line graph is a type of chart used to show information that changes over time. We plot line graphs using several points connected by straight lines. We also call it a line chart. The line graph comprises of two axes known as 'x' axis and 'y' axis. The horizontal axis is known as the x-axis.

## 5. Equations and geometry

In this lesson, we will learn how to write and solve equations using geometry concepts. We will do multiple examples involving angle relationships, perimeters, and more geometry concepts.

## 5. Systems of equations

A system of equations is a set of one or more equations involving a number of variables. The solutions to systems of equations are the variable mappings such that all component equations are satisfied—in other words, the locations at which all of these equations intersect.

## 7. Expressions with exponents

Exponential expressions are just a way to write powers in short form. The exponent indicates the number of times the base is used as a factor. So in the case of 32 it can be written as 2 × 2 × 2 × 2 × 2=25, where 2 is the “base” and 5 is the “exponent”. We read this expression as “two to the fifth power”.

## 8. Quadratics and polynomials

In algebra, a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic, is a polynomial function with one or more variables in which the highest-degree term is of the second degree.