/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 6 Observe the equations and state ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 6

Observe the equations and state the relationship being expressed. $$ x=6 y $$

Short Answer

Expert verified
Answer: x is six times greater than y.

Step by step solution

01

Identify variables

In the given equation, $$x=6 y$$, the variables are "x" and "y".
02

Analyze the relationship between variables

The relationship between x and y is given as: $$x=6 y$$. This means that x is equal to 6 times y.
03

Express the relationship

Based on the equation, the relationship between x and y is: "x is six times greater than y".

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Variables
In mathematics, variables play a significant role in understanding and expressing equations. In the equation \( x = 6y \), "x" and "y" are the variables. Each variable acts as a placeholder for numbers, allowing you to explore the relationship between varying quantities.
  • "x" represents one quantity which changes depending on the value of "y".
  • "y" represents another quantity which directly influences "x".
Understanding variables helps in substituting them with actual numbers to solve or interpret real-world situations. They enable flexibility within an equation, showing how different values can provide different outcomes. Always remember, without variables, finding such relationships would be cumbersome.
Equation Analysis
Equation analysis helps us dissect the structure and meaning of an equation. When you see an equation like \( x = 6y \), it's crucial to break it down to understand what is being communicated.
  • Start by identifying the variables involved. Here, they are "x" and "y".
  • Next, observe the mathematical operations present. This equation uses multiplication.
  • This helps us determine the relationship that "x" is six times the value of "y".
By examining the equation thoroughly, you decipher not just the direct computation involved but also the broader implications of this relationship. Equation analysis is a tool to interpret and predict how changes in one variable affect the other.
Proportional Relationships
Proportional relationships describe how one quantity scales with another. In the equation \( x = 6y \), we can see that "x" and "y" have a direct proportional relationship.
  • The term "directly proportional" means that as "y" increases or decreases, "x" does so too, at a constant rate, in this case, six times.
  • This implies that \( \frac{x}{y} = 6 \), a constant ratio.
Such relationships are often visualized as a straight line through the origin on a graph, with the slope indicating the constant rate of proportionality, here represented by 6. Recognizing proportional relationships is key in understanding linear equations, allowing you to make predictions about one variable based on changes to the other.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

List, if any should appear, the common factors for the following problems. $$ 12 x^{2} y^{3}+36 y^{3} $$

Find the domain of the equations. Assume that the independent variable is the variable that appears in the expression to the right of the equal sign. $$ k=\frac{4 t^{2}}{t-1} $$

For the following problems, simplify each of the algebraic expressions. $$ 9 a^{3} b^{7}\left(a^{3} b^{5}-2 a^{2} b^{2}+6\right)-2 a\left(a^{2} b^{7}-5 a^{5} b^{12}+3 a^{4} b^{9}\right)-a^{3} b^{7} $$

For the following problems, perform the multiplications and combine any like terms. $$ a(a-3)(a+5) $$

For the following problems, find the products. $$ \left(x+\frac{3}{4}\right)^{2} $$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.