/*! 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 45 Find the \(x\) - and \(y\) -inte... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 45

Find the \(x\) - and \(y\) -intercepts. Then graph each equation. $$ x=2 $$

Short Answer

Expert verified
The x-intercept is (2, 0); there is no y-intercept. The graph is a vertical line through x = 2.

Step by step solution

01

Identify the x-intercept

The x-intercept of a line is the point where the line crosses the x-axis. For the equation given, set y to 0 to find the x-intercept. Since the line is given by the equation x = 2, it means the line is vertical and intersects the x-axis at x = 2. Thus, the x-intercept is (2, 0).
02

Identify the y-intercept

The y-intercept of a line is the point where the line crosses the y-axis. To find the y-intercept, set x to 0. However, for the equation x = 2, no value of y will make this equation true, meaning the line does not intersect the y-axis. Thus, there is no y-intercept.
03

Graph the equation

To graph the equation x = 2, draw a vertical line that passes through the point (2, 0) on the x-axis. This line extends infinitely in both the positive and negative y directions.

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 line is the point where the line crosses the x-axis. To find this point, we set y to 0 in the equation and solve for x. For example, in the equation \(x = 2\), the line intersects the x-axis at the point \(x = 2\). Therefore, the x-intercept is \((2, 0)\). This means that no matter what the value of y is, the x-coordinate will always be 2. This results in a vertical line that crosses the x-axis right at the point \((2, 0)\).
y-intercept
The y-intercept of a line is the point where the line crosses the y-axis. To find this point, we set x to 0 in the equation and solve for y. However, with the equation \(x = 2\), there isn't a value of y that will satisfy the equation when x is 0. This is because the equation represents a vertical line at \(x = 2\), which does not cross the y-axis. Therefore, for vertical lines defined by an equation such as \(x = c\), there will be no y-intercept. This characteristic is unique to vertical lines.
vertical lines
Vertical lines and their equations have unique properties. In the equation \(x = 2\), the line is vertical and crosses the x-axis at \(x = 2\). All points on this line have the same x-coordinate of 2 but can have any y-coordinate value, extending infinitely up and down.
  • Vertical lines are always parallel to the y-axis.
  • They have no y-intercept.
  • The slope of a vertical line is undefined.
Vertical lines simplify finding x-intercepts because the vertical position does not change.
coordinate plane
The coordinate plane, also known as the Cartesian plane, is made up of an x-axis (horizontal) and a y-axis (vertical), intersecting at a point called the origin, \((0, 0)\). When graphing linear equations, understanding the coordinate plane is crucial. Each point on the plane is represented by a pair of numerical coordinates \((x, y)\).

To graph the equation \(x = 2\) on the coordinate plane:
  • Locate the point \((2, 0)\) on the x-axis.
  • Draw a vertical line that extends through \(2, 0\) and parallel to the y-axis.
This process helps visualize linear equations and their intersections with the axes.

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

If a line has slope \(-\frac{4}{9},\) then any line parallel to it has slope _____, and any line perpendicular to it has slope _____.

An equation that defines \(y\) as a function fof \(x\) is given. (a) Solve for \(y\) in terms of \(x,\) and \(r e-\) place \(y\) with the function notation \(f(x) .\) (b) Find \(f(3) .\) See Example 6. $$ y-3 x^{2}=2 $$

Find the midpoint of each segment with the given endpoints. $$ (3,-6) \text { and }(6,3) $$

Find each quotient. $$ \frac{5-7}{-4-2} $$

Suppose a factory can have no more than 200 workers on a shift, but must have at least 100 and must mamufacture at least 3000 units at minimum cost. The managers need to know how many workers should be on a shift in onder to produce the required units at minimal cost. Linear programming is a method for finding the optimal (best possible) solution that meets all the conditions for such problems. Let \(x\) represent the number of workers and y represent the mumber of units manufactured. Work Exercises \(47-52\) in order. The cost per worker is \(\$ 50\) per day and the cost to manufacture 1 unit is \(\$ 100 .\) Write an equation in \(x, y,\) and \(C\) representing the total daily cost \(C\).
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

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.