Graphs of linear equations and functions

Lisa Chen

7 min read

Listen to this study note

Study Guide Overview

This study guide covers linear equations and graphs, focusing on key concepts like slope, y-intercept, and different equation forms (slope-intercept, point-slope, and standard). It also explores graphing techniques, parallel/perpendicular lines, and real-world applications, including modeling and problem-solving. Finally, it provides practice questions and exam tips for the AP SAT (Digital).

#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:

#

Key Concept

Slope and Y-intercept: The Dynamic Duo

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.

Memory Aid

Remember: Slope is the steepness of the line and the y-intercept is where the line begins on the y-axis.

#Equations of Lines: Your Toolkit

#

Key Concept

Slope-Intercept Form

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...

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Give us your feedback and let us know how we can improve

Graphs of linear equations and functions

Lisa Chen

7 min read

Listen to this study note

Study Guide Overview

#Linear Equations and Graphs: Your Ultimate Study Guide 🚀

#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:

#

Key Concept

Slope and Y-intercept: The Dynamic Duo

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.

Memory Aid

Remember: Slope is the steepness of the line and the y-intercept is where the line begins on the y-axis.

#Equations of Lines: Your Toolkit

#

Key Concept

Slope-Intercept Form

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...

How are we doing?

Give us your feedback and let us know how we can improve