/*! 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 49 Solve each formula for \(k\) $... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 49

Solve each formula for \(k\) $$ y=k x $$

Short Answer

Expert verified
k = y / x.

Step by step solution

01

Understand the Equation

The given equation is the linear equation y = k x. We need to solve this for the variable k.
02

Isolate the Variable k

To isolate k, we need to get k by itself on one side of the equation. To do this, divide both sides of the equation by x. This yields:y / x = k x / x.
03

Simplify the Equation

Now simplify the right side of the equation:y / x = k. Thus, we have isolated k.

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.

linear equations
A linear equation is a simple, yet fundamental type of algebraic expression. It can be written in the form of ax + b = 0 or similar variations. In the specific exercise, the linear equation is given as y = kx.
Linear equations have the following characteristics:
  • They graph as straight lines on a Cartesian plane.
  • They have a constant rate of change.
Understanding linear equations is crucial for solving for unknown variables and analyzing relationships between them.
isolating variables
Isolating a variable means manipulating an equation to get the variable alone on one side. In the exercise, we aim to solve for the variable k.
To isolate k, you should follow these steps:
  • Identify the variable you need to isolate.
  • Perform algebraic operations to remove other terms or coefficients.
  • Ensure that you perform the same operations on both sides of the equation to keep it balanced.
For instance, in the given equation y = kx, we need to isolate k by dividing both sides by x.
algebraic manipulation
Algebraic manipulation involves performing operations to rearrange and simplify equations. These are the tools you'll often use:
  • Addition/Subtraction: Used to move terms from one side of an equation to the other.
  • Multiplication/Division: Used to eliminate coefficients or to isolate variables.
  • Distribution: Involves multiplying through parentheses to simplify expressions.
In the given problem, we use division to simplify and isolate the variable k. Mastering these manipulations is key to solving various types of equations.
division in equations
Division is used to solve for a variable when that variable is multiplied by another term. For the equation y = kx, we divide both sides by x to solve for k.
The steps are:
  • Identify the multiplication relationship involving the variable you need to isolate.
  • Divide both sides of the equation by the same non-zero term to maintain equality.
  • Simplify the resulting equation.
So, in this problem, we perform the division y/x = k, which isolates k effectively. Understanding when and how to use division is vital for manipulating equations correctly.

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

Solve each problem. In a certain fraction, the denominator is 6 more than the numerator. If 3 is added to both the numerator and the denominator, the resulting fraction is equivalent to \(\frac{5}{7} .\) What was the original fraction (not written in lowest terms)?

Exercises \(61-82 \text { involve factoring by grouping (Section } 6.1)\) and factoring sums and differences of cubes (Section 6.4). Write each rational expression in lowest terms. $$ \frac{1+p^{3}}{1+p} $$

Find the LCD for the fractions in each list. $$ \frac{12}{m^{7}}, \frac{14}{m^{8}} $$

Simplify each fraction. $$ \frac{1+t^{-1}-56 t^{-2}}{1-t^{-1}-72 t^{-2}} $$

One roofer can put a new roof on a house three times faster than another. Working to- gether, they can roof a house in 4 days. How long would it take the faster roofer working alone?
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics 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.