Proportional Relationships - Varsity Tutors

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Proportional Relationships

Study Guide

Key Definition

A proportional relationship is one in which two quantities vary directly with each other. If $y = kx$ for some constant $k$, then $k$ is called the constant of proportionality.

Important Notes

  • The graph of $y = kx$ is a straight line through the origin
  • The ratio $\frac{y}{x}$ is constant
  • If $x$ increases, $y$ increases (for positive $k$)
  • If $x$ decreases, $y$ decreases (for positive $k$)
  • Proportional relationships imply linear graphs

Mathematical Notation

$y = kx$ represents a proportional relationship$k$ is the constant of proportionalityRemember to use proper notation when solving problems

Why It Works

Proportional relationships maintain a constant ratio $\frac{y}{x} = k$, ensuring the relationship is linear.

Remember

Always check if the ratio $\frac{y}{x}$ is constant to verify proportionality.

Quick Reference

Proportional Equation:$y = kx$

Understanding Proportional Relationships

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Video explanation of this concept

concept. Use space or enter to play video.concept thumbnailBeginner

Start here! Easy to understand

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Beginner Explanation

A simple relationship where $y = kx$, and $k$ is a constant representing the rate of change between y and x.Now showing Beginner level explanation.

Practice Problems

Test your understanding with practice problems

1

Quick Quiz

Single Choice QuizBeginner

What is $y$ when $x = 12$ and $k = \frac{1}{3}$?

A$4$B$3$C$5$D$6$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.2

Real-World Problem

Question ExerciseIntermediate

Teenager Scenario

A car travels at a constant speed. If it covers $24$ miles in $3$ hours, find the speed in miles per hour.Show AnswerClick to reveal the detailed solution for this question exercise.3

Thinking Challenge

Thinking ExerciseIntermediate

Think About This

If $y = 30$ when $x = 6$, what is $y$ when $x = 100$?

Show AnswerClick to reveal the detailed explanation for this thinking exercise.4

Challenge Quiz

Single Choice QuizAdvanced

Given $y = kx$, find k if $y = 45$ and $x = 9$.

A$5$B$4$C$6$D$3$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.

Recap

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Review key concepts and takeaways

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