/*! 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 21 Find the \(x\) - and \(y\) -inte... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 21

Find the \(x\) - and \(y\) -intercepts of the equation. $$x-4=3 y$$

Short Answer

Expert verified
The x-intercept is (4, 0) and the y-intercept is (0, -\frac{4}{3}).

Step by step solution

01

Rewrite the Equation

Rewrite the given linear equation in the form of y = mx + b. Start by isolating y. The given equation is: $$x - 4 = 3y$$Add 4 to both sides:$$x = 3y + 4$$Next, subtract 4 from both sides:$$x - 4 = 3y$$Finally, divide both sides by 3:$$y = \frac{x - 4}{3}$$
02

Find the x-intercept

To find the x-intercept, set y to 0 and solve for x. Start with the equation:$$x - 4 = 3(0)$$This simplifies to:$$x - 4 = 0$$Add 4 to both sides:$$x = 4$$Therefore, the x-intercept is at (4, 0).
03

Find the y-intercept

To find the y-intercept, set x to 0 and solve for y. Start with the equation:$$0 - 4 = 3y$$This simplifies to:$$-4 = 3y$$Divide both sides by 3:$$y = -\frac{4}{3}$$ Therefore, the y-intercept is at (0, -\frac{4}{3}).

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.

x-intercept
The x-intercept is where the graph of a linear equation crosses the x-axis. This point is crucial because it gives one of the key values of the equation. To find the x-intercept, set y to 0 in the equation and solve for x.

Let's look at our equation: \(x - 4 = 3y\).
When we set y to 0, the equation becomes \(x - 4 = 3(0)\).
This simplifies to \(x - 4 = 0\).
;To isolate x, add 4 to both sides: \(x = 4\).
Hence, the x-intercept of the equation \(x - 4 = 3y\) is at (4, 0).

Understanding the x-intercept helps in plotting the graph accurately and analyzing the behavior of the equation across different values of x.
y-intercept
The y-intercept is where the graph crosses the y-axis. This point is fundamental as it shows the value of y when x is 0. To find it, set x to 0 in the equation and solve for y.

For our given equation, \(x - 4 = 3y\),
we set x to 0: \(0 - 4 = 3y\).
This simplifies to \(-4 = 3y\).
Now, divide both sides by 3 to isolate y: \(y = -\frac{4}{3}\).
Thus, the y-intercept of the equation \(x - 4 = 3y\) is at (0, -\frac{4}{3}).

Knowing the y-intercept allows us to plot the starting point on the y-axis, aiding in sketching the overall graph of the linear equation.
solving linear equations
Solving linear equations often involves several steps to isolate the variable of interest. Here's a more detailed look at how to approach it using our example equation, \(x - 4 = 3y\):
  • First, rewrite the equation in a more conventional form (y = mx + b), which is known as the slope-intercept form. This helps in identifying the slope and intercepts easily.
  • Start by isolating y on one side of the equation. Add 4 to both sides: \(x = 3y + 4\).
  • Then, subtract 4 from both sides to bring the equation into one step closer to isolating y: \(x - 4 = 3y\).
  • Finally, divide every term by 3: \(y = \frac{x - 4}{3}\). Now your equation is in the y = mx + b form, where \(m\) is the slope and \(b\) is the y-intercept.

Steps like these are essential in simplifying and solving linear equations. These steps ensure that each part of the equation is correctly handled. This ensures that we get accurate intercepts and are able to graph the linear relationship effectively. Breaking down the steps helps in better understanding and application.

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 of the following problems algebraically. Be sure to label what the variable represents. The width of a rectangle is 4 less than \(\frac{2}{3}\) its length. If the perimeter of the rectangle is 3 times the length, find its dimensions.

Sketch the graph of \(u-4 v=8\) using the horizontal axis for \(u\) values and the vertical axis for \(v\) values.

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

Solve each of the following problems algebraically. Be sure to label what the variable represents. Marina does one third of her homework problems when she comes home, 8 problems just before supper, and the remaining two fifths of the problems after supper. How many homework problems did she have?

Write an equation of the line satisfying the given conditions. Passing through \((-1,4)\) and \((2,-2)\)
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Geometry

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.