Algebra 1 Midterm Study Guide

These flashcards cover key concepts from the Algebra 1 midterm study guide, including properties of real numbers, solving equations, and graphing.

What are the characteristics of rational numbers in the real number system?

Rational numbers either end or repeat as decimals.

What distinguishes irrational numbers from rational numbers?

Irrational numbers neither end nor repeat as decimals.

Name the properties of real numbers.

Commutative, Associative, Identity (multiplication & additive), Inverse (multiplicative & additive), Property of zero (multiplication by), Distributive.

What is the substitution property in algebra?

This property allows for the replacement of a variable in an expression with a number.

What is the process to simplify an expression involving like terms?

Add like terms together, which are terms with the same variables and exponents.

Explain what a multi-step equation is.

An equation that requires more than one step to solve, often involving multiple operations.

What does it mean when an equation has a unique solution?

It means there is exactly one solution to the equation.

What is an absolute value equation?

An equation that includes an absolute value expression.

What is the slope formula used for?

To calculate the slope of a line given two points: m = (y₂ − y₁) / (x₂ − x₁).

How do you convert a linear equation into slope-intercept form?

Transform the equation into the format y = mx + b, where m is the slope and b is the y-intercept.

What is the intercept method for graphing equations?

Using x and y intercepts to plot the graph of the equation.