Complete Algebra I Course: In-Depth
Notes and Study Guide
Unit 1: Expressions, Equations & Inequalities
• A **variable** is a letter that represents an unknown number (like x or y).
• A **constant** is a number on its own (like 3, -7, or 0.5).
• A **coefficient** is a number that multiplies a variable (like 4 in 4x).
• An **expression** is a math phrase made of numbers, variables, and operations (like
2x + 3).
• An **equation** has an equals sign and shows two things are equal (like 2x + 3 = 7).
• An **inequality** compares two values (like x > 5 or x ≤ 2).
• To **simplify expressions**, use the distributive property and combine like terms.
• **Solving equations** means finding the value of the variable that makes the equation
true.
• Use **inverse operations** (opposite operations) to isolate the variable.
• Inequalities are solved like equations, but if you multiply or divide by a negative
number, you must flip the inequality sign.
Unit 2: Linear Equations & Functions
• A **linear equation** forms a straight line when graphed.
• The **slope** (m) tells how steep the line is: rise over run.
• The **y-intercept** (b) is where the line crosses the y-axis.
• **Slope-Intercept Form**: y = mx + b.
• **Standard Form**: Ax + By = C.
• **Point-Slope Form**: y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line.
• To graph: find the y-intercept, use the slope to find more points, and draw the line.
• Use a **table** or plug in x-values to get y-values for graphing.
• **Slope formula**: m = (y₂ - y₁) / (x₂ - x₁).
Unit 3: Systems of Equations & Inequalities
• A **system of equations** is two or more equations with the same variables.
• **Graphing method**: Graph both lines. The intersection is the solution.
• **Substitution method**: Solve one equation for one variable and plug it into the
other.
• **Elimination method**: Add or subtract equations to eliminate one variable.
• For systems of inequalities, graph each one and shade the correct region. The solution
is where shaded regions overlap.
Notes and Study Guide
Unit 1: Expressions, Equations & Inequalities
• A **variable** is a letter that represents an unknown number (like x or y).
• A **constant** is a number on its own (like 3, -7, or 0.5).
• A **coefficient** is a number that multiplies a variable (like 4 in 4x).
• An **expression** is a math phrase made of numbers, variables, and operations (like
2x + 3).
• An **equation** has an equals sign and shows two things are equal (like 2x + 3 = 7).
• An **inequality** compares two values (like x > 5 or x ≤ 2).
• To **simplify expressions**, use the distributive property and combine like terms.
• **Solving equations** means finding the value of the variable that makes the equation
true.
• Use **inverse operations** (opposite operations) to isolate the variable.
• Inequalities are solved like equations, but if you multiply or divide by a negative
number, you must flip the inequality sign.
Unit 2: Linear Equations & Functions
• A **linear equation** forms a straight line when graphed.
• The **slope** (m) tells how steep the line is: rise over run.
• The **y-intercept** (b) is where the line crosses the y-axis.
• **Slope-Intercept Form**: y = mx + b.
• **Standard Form**: Ax + By = C.
• **Point-Slope Form**: y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line.
• To graph: find the y-intercept, use the slope to find more points, and draw the line.
• Use a **table** or plug in x-values to get y-values for graphing.
• **Slope formula**: m = (y₂ - y₁) / (x₂ - x₁).
Unit 3: Systems of Equations & Inequalities
• A **system of equations** is two or more equations with the same variables.
• **Graphing method**: Graph both lines. The intersection is the solution.
• **Substitution method**: Solve one equation for one variable and plug it into the
other.
• **Elimination method**: Add or subtract equations to eliminate one variable.
• For systems of inequalities, graph each one and shade the correct region. The solution
is where shaded regions overlap.
