SAT Math

A comprehensive course to master all the mathematical concepts, skills, and strategies needed to succeed on the SAT exam.

Numbers and OperationsAlgebraic Expressions and EquationsLinear Functions and Graphs
Quadratic Functions and ParabolasSystems of EquationsData Analysis and Statistics
Budgeting and Financial MathDistance, Rate, and Time ProblemsGeometry in Construction and Design
Plugging In NumbersBacksolving Answer Choices
Numbers and Operatio...Algebraic Expression...Linear Functions and...Quadratic Functions ...Systems of EquationsData Analysis and St...Budgeting and Financ...Distance, Rate, and ...Geometry in Construc...Plugging In NumbersBacksolving Answer C...
Basic Concepts

Linear Functions and Graphs

What is a Linear Function?

A linear function is any function that graphs as a straight line. It’s usually written as \( y = mx + b \), where:

  • \( m \) is the slope (how steep the line is)
  • \( b \) is the y-intercept (where the line crosses the y-axis)

Interpreting Graphs

Being able to quickly read and interpret graphs is crucial for the SAT. Look for where lines intersect, their slopes, and what the axes represent.

Real-World Applications

Linear functions appear in budgeting, distance vs. time problems, and anything with a constant rate of change.

Tips for Success

  • Find slope by picking two points: \( m = \frac{y_2 - y_1}{x_2 - x_1} \)
  • The y-intercept is where \( x = 0 \)

Examples

  • Finding the slope between (2, 3) and (4, 7): \( m = \frac{7 - 3}{4 - 2} = 2 \)

  • Graphing \( y = -2x + 5 \) starts at (0, 5) and goes down 2 units for every 1 unit right.

In a Nutshell

Understand how to work with linear functions and interpret their graphs.

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Quadratic Functions and Parabolas