/*! 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 17 Find the \(x\) - and \(y\) -inte... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 17

Find the \(x\) - and \(y\) -intercepts of the equation. $$2 x=5 y$$

Short Answer

Expert verified
Both x- and y-intercepts are at (0, 0).

Step by step solution

01

Understanding the Equation

The given equation is \[ 2x = 5y \]. To find the intercepts, determine where the line crosses the x-axis and y-axis.
02

Find the x-intercept

To find the x-intercept, set \(y = 0\) in the equation and solve for \(x\). \[ 2x = 5(0) \] \[ 2x = 0 \] \[ x = 0 \] The x-intercept is at \((0, 0)\).
03

Find the y-intercept

To find the y-intercept, set \(x = 0\) in the equation and solve for \(y\). \[ 2(0) = 5y \] \[ 0 = 5y \] \[ y = 0 \] The y-intercept is at \((0, 0)\).
04

Interpret the Results

Both the x-intercept and y-intercept of the equation \(2x = 5y\) are the same. The line crosses the origin at point \((0, 0)\).

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 an equation that plots a straight line on a graph. These equations typically take the form of \(Ax + By = C\) where \(A\), \(B\), and \(C\) are constants. Linear equations are fundamental in algebra and are used in various fields such as physics, economics, and engineering. In the given equation \(2x = 5y\), we are dealing with a linear relationship between \(x\) and \(y\). A crucial property of linear equations is that they yield graphs that are straight lines, which can be defined completely by two main points: the intercepts.
Solving for Intercepts
Intercepts are points where the graph of an equation crosses the x-axis and y-axis. They offer a very useful way to understand the behavior of linear functions. To find the intercepts of the equation \(2x = 5y\):
  • x-intercept: Set \(y = 0\) and solve for \(x\)
  • y-intercept: Set \(x = 0\) and solve for \(y\)

For the equation \(2x = 5y\):
1. Set \(y = 0\):
\(2x = 5(0)\)
\(2x = 0\)
\(x = 0\)
The x-intercept is \((0, 0)\).
2. Set \(x = 0\):
\(2(0) = 5y\)
\(0 = 5y\)
\(y = 0\)
The y-intercept is \((0, 0)\).
In this case, both intercepts occur at the same point, the origin \((0, 0)\).
Algebra
Algebra involves working with mathematical symbols to solve problems. It's an essential branch of mathematics that introduces using variables to represent numbers. In our problem, we solve the equation \(2x = 5y\) by substituting values for \(x\) and \(y\) to find the intercepts.
Key skills in algebra include:
  • Manipulating equations: Adding, subtracting, multiplying, or dividing both sides of equations to isolate the variable of interest
  • Substitution: Plugging in values for known variables to solve for unknowns
  • Simplifying: Reducing expressions to their simplest form to make calculations easier

When we set \(y = 0\) to find the x-intercept and \(x = 0\) to find the y-intercept, we use these key algebraic principles to solve the problem step by step. Algebra helps us to systematically understand and find solutions to mathematical problems, making it a powerful tool in both simple and complex scenarios.

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

Sketch the graph of the line satisfying the given conditions. Passing through \((2,1)\) with slope \(\frac{2}{3}\)

Sketch the graph of the line satisfying the given conditions. Passing through \((-1,-5)\) and whose slope is undefined

Solve the following problem algebraically. Be sure to label what the variable represents. Tamika leaves point \(A\) at 10: 00 A.M. traveling due east at 60 kph. One-half hour later, Ramon leaves the same location traveling due west at \(70 \mathrm{kph}\). At what time will they be \(257.5 \mathrm{km}\) apart?

Round off to the nearest hundredth when necessary. Bridges (and many concrete highways) are constructed with "expansion joints," which are small gaps in the roadway between one section of the bridge and the next. These expansion joints allow room for the roadway to expand during hot weather. Suppose that a bridge has a gap of \(1.5 \mathrm{cm}\) when the air temperature is \(24^{\circ} \mathrm{C},\) that the gap narrows to \(0.7 \mathrm{cm}\) when the air temperature is \(33^{\circ} \mathrm{C},\) and that the width of the gap is linearly related to the temperature. (a) Write an equation relating the width of the gap \(w\) and the temperature \(t\) (b) What would be the width of a gap in this roadway at \(28^{\circ} \mathrm{C} ?\) (c) At what temperature would the gap close completely? (d) If the temperature exceeds the value found in part (c) that causes the gap to close, it is possible that the roadway could buckle. Is this likely to occur? Explain.

Determine the slope of the line from its equation. $$x+y=7$$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Statistics

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.