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Linear relationship word problems

Jessica White

Jessica White

6 min read

Study Guide Overview

This guide covers linear relationships for the AP SAT (Digital) exam, focusing on slope (rate of change), y-intercept (starting point), and modeling with linear equations (y = mx + b). It explains how to set up equations from points, slopes, and verbal descriptions, and how to solve and interpret them in real-world contexts. The guide also emphasizes identifying variables, analyzing relationships, and provides practice questions with a scoring breakdown.

Linear Relationships: Your Guide to Conquering Word Problems πŸš€

Hey there! Ready to make word problems your playground? This guide is your go-to for mastering linear relationships, packed with everything you need for the AP SAT (Digital) exam. Let's dive in!

Understanding Linear Relationships

Linear relationships are all about that straight-line action! They help us connect real-world scenarios to math equations, showing how things change at a constant rate. Think of it as your math superpower for everyday life. Let's break it down:

Key Concept

Slope: The Rate of Change

  • What it is: Slope (often represented by 'm') shows how much the dependent variable (y) changes for every one unit increase in the independent variable (x).
  • Real-world examples:
    • Car rental: Slope = cost per mile driven
    • Business: Slope = profit increase per unit sold
  • Types of slopes:
    • Positive slope: Direct relationship (as x increases, y increases)
    • Negative slope: Inverse relationship (as x increases, y decreases)
  • Steeper slope: Faster rate of change

Key Concept

Y-intercept: The Starting Point

  • What it is: The y-intercept (often represented by 'b') is the value of the dependent variable (y) when the independent variable (x) is zero.
  • Real-world examples:
    • Car rental: Y-intercept = fixed base rental fee
    • Savings account: Y-intercept = initial deposit amount
    • Note: Sometimes, a y-intercept might be a theoretical starting point if x=0 isn't practical.

Modeling with Linear Equations

Setting Up Equations: T...