#Linear Equations and Graphs: Your Ultimate Study Guide 🚀

Hey there! Let's get you prepped for the AP SAT (Digital) with a super focused review of linear equations and graphs. This is a BIG topic, so let’s make sure you’re totally comfortable with it. Think of this as your go-to resource for acing those questions!

#Understanding the Basics

Linear equations and functions are all about straight lines. They show how two variables relate, and mastering them is crucial for the exam. Let's break it down:

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• Slope (m): The rate of change. How much does 'y' change for every change in 'x'?

  • Rise over run: Vertical change / Horizontal change. Think of it as climbing a hill (or going down one!).
  • Positive slope: Line goes up from left to right. ↗️
  • Negative slope: Line goes down from left to right. ↘️
  • Zero slope: Horizontal line. ↔️
  • Undefined slope: Vertical line. ↕️

• Y-intercept (b): Where the line crosses the y-axis. It's the 'y' value when 'x' is zero. Often your starting point or initial value.

#Equations of Lines: Your Toolkit

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• Equation: $$y = mx + b$$
  • m is the slope.
  • b is the y-intercept.
  • Super useful when you know the slope and y-intercept directly from the graph.

#Point-Slope Form

• Equation: $$y - y₁ = m(x - x₁)$$
  • (x₁, y₁) is a point on the line.
  • m is the slope.
  • Great when you have a point and...