/*! 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 48 Find the \(x\) - and \(y\) -inte... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 48

Find the \(x\) - and \(y\) -intercepts. Then graph each equation. $$ x-4=0 $$

Short Answer

Expert verified
The x-intercept is (4, 0) and there is no y-intercept. The graph is a vertical line at x = 4.

Step by step solution

01

Solve for x-intercept

To find the x-intercept, set y to 0 and solve for x. In the equation provided, there is no y term, which means it is already isolated for x. The equation is: divdefinition: When you set y to 0, your equation becomes: divnumberedvars: setting y=xy-4=4. The solution is x=x=4.divexample: So,replace the y=0,x=x-4.This means the x-intercept is at point (4, 0).
02

Solve for y-intercept

To find the y-intercept, set x to 0 and solve for y. However, since the equation does not contain a y term, it indicates there is no y-intercept for this line. Mathematically, substituting x=0 in the equation results in: divdefinition: As there is no y term in the equation, there are no y values that the line will cross. So, the y-intercept does not exist.
03

Graph the equation

Plot the point where the line crosses the x-axis at (4, 0). Since there is no y-intercept and the equation indicates x is always 4, draw a vertical line passing through the x-coordinate 4.

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 of a linear equation is the point where the line crosses the x-axis. To find this point, you set the y-value to 0 and solve for x. In the equation provided, \(x - 4 = 0\), there is no y term, so we don't need to worry about setting y to 0.We simply solve the equation for x:
\( x - 4 = 0 \)
Solve for x by adding 4 to both sides:
\( x = 4 \)
This means that the x-intercept is at the point (4, 0).
  • Remember: Set y to 0 to find the x-intercept.
  • The result will give you the x-coordinate of your intercept.
In this specific equation, because y does not appear, simplifying the equation tells us directly that x is always 4, which places the x-intercept at (4, 0).
y-intercept
The y-intercept is where the line crosses the y-axis. To find this point, set x to 0 and solve for y. However, in our example equation:\( x - 4 = 0 \), there is no y term present. This tells us a key piece of information about the line:
  • Since no matter what value y takes, x is always going to be 4, the line never crosses the y-axis.
  • You can think of this as a vertical line that does not interact with the y-axis.
Therefore, for this equation, there is no y-intercept.
When an equation of a line lacks a y term, it indicates that the line runs parallel to the y-axis.
solving linear equations
Solving linear equations involves finding values for the variables that make the equation true. Here, we've already addressed finding where the line intersects the axes, but let's discuss how to solve linear equations in general:First, identify what is asked:
  • Are you solving for x? Set y to 0 and solve the equation.
  • Or solving for y? Set x to 0 and solve the equation.
To solve our specific equation \( x - 4 = 0 \):
1. Isolate the variable you're solving for (x):
\( x - 4 = 0 \)
In this case, we add 4 to both sides:
\( x = 4 \)
2. Verify the solution: Substitute it back into the original equation to ensure it holds true.
  • For this equation: *Verification isn't needed, as setting x to 4 is straightforward*.
For more complex linear equations, you might need steps like:
  • Combining like terms
  • Using the distributive property
  • Checking for multiple variables
But the basic principle remains the same: simplify until you isolate the variable.

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

Find an equation of the line passing through the given points. (a) Write the equation in standard form. (b) Write the equation in slope-intercept form if possible. $$ (7,6) \text { and }(7,-8) $$

Solve each problem. Federal regulations set standards for the size of the quarters of marine mammals. A pool to house sea otters must have a volume of "the square of the sea otter's average adult length (in meters) multiplied by 3.14 and by 0.91 meter." If \(x\) represents the sea otter's average adult length and \(f(x)\) represents the volume (in cubic meters) of the corresponding pool size, this formula can be written as $$ f(x)=0.91(3.14) x^{2} $$

For each situation, (a) write an equation in the form \(y=m x+b,(b)\) find and interpret the ordered pair associated with the equation for \(x=5,\) and \((c)\) answer the question. Another cell phone plan includes 450 anytime minutes for \(\$ 40\) per month, plus \(\$ 50\) for a Nokia 2320 cell phone and \(\$ 36\) for a one-time activation fee. (Source: AT\&T.) Let \(x\) represent the number of months of service and \(y\) represent the cost. If you sign a 1 -yr contract, how much will this cell phone plan cost? (Assume that you never use more than the allotted number of minutes.)

For each situation, (a) write an equation in the form \(y=m x+b,(b)\) find and interpret the ordered pair associated with the equation for \(x=5,\) and \((c)\) answer the question. For a family membership, the athletic club in Exercise 83 charges a membership fee of S159, plus \(\$ 60\) for each additional family member after the first. Let \(x\) represent the number of additional family members and \(y\) represent the cost. What is the membership fee for a four-person family?

Solve each equation for \(y\). $$ 4 x-y=10 $$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Calculus

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.