Algebra 1 Study Guide: Equations, Graphing, and Practice Test

Algebra 1 Study Guide: Equations, Graphing, and Practice
Test
This guide covers key Algebra 1 skills for solving equations, graphing linear
relationships, and applying concepts to word problems. It includes
explanations, formulas, worked examples, and a 40-question practice test
with answers.


Table of Contents
1. Key Formulas and Vocabulary
2. Solving Equations
3. Graphing Linear Equations
4. Word Problems and Applications
5. Practice Test
6. Answer Key with Brief Solutions
7. Common Mistakes and Test Tips


1. Key Formulas and Vocabulary

Concept Formula / Rule

𝑦2 − 𝑦1
Slope 𝑚=
𝑥2 − 𝑥1

Slope-Intercept Form 𝑦 = 𝑚𝑥 + 𝑏

Point-Slope Form 𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1 )

, Concept Formula / Rule

Standard Form 𝐴𝑥 + 𝐵𝑦 = 𝐶

Parallel Lines Same slope: 𝑚1 = 𝑚2

Perpendicular Lines Negative reciprocal slopes: 𝑚1 ⋅ 𝑚2 = −1


Distance 𝑑 = √(𝑥2 − 𝑥1 )2 + (𝑦2 − 𝑦1 )2

𝑥 +𝑥 𝑦 +𝑦
Midpoint ( 1 2 2 , 1 2 2)

Vocabulary
• Variable: a letter representing an unknown number.
• Coefficient: the number multiplied by a variable.
• Constant: a number without a variable.
• Equation: a mathematical statement that two expressions are equal.
• Inequality: a statement comparing expressions using <, >, ≤, ≥.
• Solution: a value that makes an equation true.
• Intercept: where a graph crosses an axis.
• Slope: steepness of a line; rise over run.


2. Solving Equations
A. One-Step Equations
Example: 𝑥 + 7 = 12
Subtract 7 from both sides: 𝑥 = 5