/*! 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 22 Find the \(x\) - and \(y\) -inte... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 22

Find the \(x\) - and \(y\) -intercepts. Then graph each equation. $$ x=-3 $$

Short Answer

Expert verified
x-intercept is \((-3, 0)\); no y-intercept; graph is a vertical line at \(x = -3\).

Step by step solution

01

Identify the given equation

The equation provided is a vertical line given by the equation \(x = -3\). This indicates that for all points on the line, the value of \(x\) is -3.
02

Find the x-intercept

For a vertical line, the x-intercept is where the line crosses the x-axis. So, we set \(y = 0\) and solve for \(x\):\(x = -3\).The x-intercept is at \((-3, 0)\).
03

Find the y-intercept

A vertical line does not cross the y-axis unless it is the y-axis itself (i.e., \(x = 0\)). Therefore, this vertical line has no y-intercept.
04

Graph the equation

Plot the vertical line \(x = -3\) on a Cartesian plane by drawing a straight line that passes through \((-3, y)\) for all values of \(y\). The line will be parallel to the y-axis.

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
To understand the concept of the x-intercept, think about where a graph crosses the x-axis. The x-axis is the horizontal line in a graph. The x-intercept is where the line meets this axis. This means at this point, the y-value is always zero.

For example, if you want to find the x-intercept of the vertical line given by the equation \(x = -3\), set y to zero and solve for x. Here, the equation simplifies directly to \(x = -3\). So, the x-intercept is the point \((-3, 0)\).
It's important to note that for vertical lines like \(x = -3\), the x-intercept is a point right on the line. This is where it crosses the x-axis.
y-intercept
Now let's look at the y-intercept. This is where the graph crosses the y-axis. The y-axis is the vertical line in a graph. The y-intercept means the x-value at this point is always zero.

However, for the equation \(x = -3\), which represents a vertical line, there's a unique situation. A vertical line like this one runs parallel to the y-axis and never actually touches it.
Hence, it doesn't have a y-intercept. It might be tricky at first, but remember that vertical lines only include x-intercepts unless they specifically cross the y-axis.
vertical line graph
Graphing a vertical line is straightforward once you understand the basics.

The equation of a vertical line is always in the form \(x = a\), which means that x is a constant value. In our example, the vertical line is \(x = -3\). To draw this line on a graph:
  • Find \(-3\) on the x-axis.
  • Draw a straight line parallel to the y-axis passing through this point. This line will never cross the y-axis.
  • Every point on this line has an x-coordinate of \(-3\).
Vertical lines are one of the simplest forms of equations to graph since they do not change in the y-direction.

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

The average price of a gallon of unleaded gasoline in 2000 was \(\$ 1.51 .\) In 2016 , the average price was \(\$ 2.14 .\) Find and interpret the average rate of change in the price of a gallon of gasoline per year to the nearest cent. (Data from Energy Information Administration.)

Three kinds of tickets are available for a rock concert: "up close," "in the middle," and "far out." "Up close" tickets cost \(\$ 10\) more than "in the middle" tickets. "In the middle" tickets cost \(\$ 10\) more than "far out" tickets. Twice the cost of an "up close" ticket is \(\$ 20\) more than three times the cost of a "far out" ticket. Find the price of each kind of ticket.

A wholesaler supplies college t-shirts to three college bookstores: \(\mathrm{A}, \mathrm{B},\) and \(\mathrm{C} .\) The wholesaler recently shipped a total of \(800 \mathrm{t}\) -shirts to the three bookstores. Twice as many t-shirts were shipped to bookstore \(\mathrm{B}\) as to bookstore \(\mathrm{A},\) and the number shipped to bookstore \(\mathrm{C}\) was 40 less than the sum of the numbers shipped to the other two bookstores. How many t-shirts were shipped to each bookstore?

How many gallons each of \(25 \%\) alcohol and \(35 \%\) alcohol should be mixed to obtain 20 gal of \(32 \%\) alcohol?

Graph each line passing through the given point and having the given slope $$ (-3,1) ; \text { undefined slope } $$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

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.