Core Concepts

• Understand and evaluate function notation \( f(x) \)
• Interpret function values in real-world contexts (e.g., cost, distance)
• Identify linear functions by their form \( y = mx + b \)
• Distinguish from exponential or quadratic equations

Graphing Linear Equations

• Plot the y-intercept and use the slope to find additional points
• Identify x-intercepts and their meaning in context
• Recognize increasing and decreasing lines

Slope and Rate of Change

• Calculate slope from two points: \( m = \frac{y_2 - y_1}{x_2 - x_1} \)
• Interpret slope in context (e.g., rate, change)
• Understand types of slope: positive, negative, zero, undefined

Writing Equations of Lines

• Use slope-intercept form: \( y = mx + b \)
• Use point-slope form: \( y - y_1 = m(x - x_1) \)
• Write equations from verbal or written problem descriptions

Parallel and Perpendicular Lines

• Parallel lines: same slope
• Perpendicular lines: slopes are negative reciprocals

Linear Models and Applications

• Create models from scenarios (e.g., budgeting, savings)
• Use models to estimate or predict outcomes

Interpreting Graphs

• Identify intercepts and slope visually
• Extract rules and features from a table or graph

Solving for Intercepts

• Set \( y = 0 \) to find x-intercepts
• Set \( x = 0 \) to find y-intercepts
• Apply to real-world problems

Piecewise Functions

• Understand when different rules apply in different intervals
• Evaluate function values based on domain boundaries

SAT-Specific Strategies

• Translate word problems into linear functions
• Use tables to confirm constant rate of change
• Determine function rules based on patterns

Function Composition & Systems

• Understand and evaluate \( f(g(x)) \)
• Solve systems of equations algebraically or graphically
• Find points of intersection between multiple linear functions