/*! 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 86 In the following exercises, grap... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Problem 86

In the following exercises, graph the vertical and horizontal lines. $$ x=-5 $$

Short Answer

Expert verified
Graph a vertical line at \( x = -5 \).

Step by step solution

01

Identify the Given Equation

The equation provided is given as \( x = -5 \). This states that for any value of \( y \), \( x \) will always be \( -5 \).
02

Determine the Nature of the Line

The equation \( x = -5 \) is that of a vertical line. Vertical lines have a constant \( x \text{-coordinate} \) irrespective of the \( y \text{-coordinate} \).
03

Plot Points for the Line

To graph this line, choose any values for \( y \) and set \( x = -5 \). For example: - (\( -5, 0 \)) - (\( -5, 2 \)) - (\( -5, -3 \)).
04

Draw the Vertical Line

On a graph, plot the points (\( -5, 0 \)), (\( -5, 2 \)), and (\( -5, -3 \)). Connect these points with a straight vertical line.
05

Check and Label the Graph

Ensure the line passes through all points where \( x = -5 \). Label the line as \( x = -5 \).

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.

Vertical Lines
A vertical line on a graph is a line that goes straight up and down, parallel to the y-axis. In mathematical terms, a vertical line has an equation of the form x = a where 'a' is a constant. This means that for any value of y, the x-value will always be the same鈥攊n this case, -5. Consider the example line with the equation x = -5. No matter what y-value you pick, the x-value stays at -5. This creates a vertical line on the graph. Vertical lines are unique because they have an undefined slope, making them distinct from horizontal or slanted lines.
Graph Plotting
Graph plotting is a crucial skill in algebra and geometry. When plotting a graph, you start by drawing the axes: the horizontal x-axis and the vertical y-axis. Each axis is marked with evenly spaced numbers. To plot a point, locate its x and y coordinates and mark where they meet on the graph. In the case of plotting the vertical line x = -5, you'll follow these steps:
  • Identify the x-coordinate, which is always -5.
  • Choose any y-value, such as 0, 2, or -3.
  • Plot the points (-5, 0), (-5, 2), and (-5, -3) on the graph.
  • Connect the points with a straight vertical line.
Remember, the vertical line will pass through all points where x is -5.
Cartesian Coordinates
The Cartesian coordinate system is a way to uniquely determine the position of points on a plane. Named after Ren茅 Descartes, it uses two perpendicular axes: the x-axis (horizontal) and the y-axis (vertical). Each point on the plane is represented by a pair of numbers (x, y), called the coordinates. The x-coordinate tells you how far to move right or left from the origin (0,0), while the y-coordinate tells you how far to move up or down. For instance, the coordinates (-5, 2) mean you move 5 units to the left and 2 units up from the origin. In graphing the line x = -5, all points will have -5 as the x-coordinate, and varying values for y.
Linear Equations
Linear equations represent straight lines on a graph and can come in various forms. The most common form is the slope-intercept form y = mx + b where 'm' is the slope and 'b' is the y-intercept. Another form is the standard form Ax + By = C. Vertical lines, such as x = -5, are a special type of linear equation where the x-value remains constant, and the slope is undefined. To graph a vertical line, you only need to plot points where x is the given constant and y varies. The simplicity of linear equations makes them foundational for more advanced math topics.

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

In the following exercises, graph by plotting points. $$ -x+y=3 $$

In the following exercises, graph the vertical and horizontal lines. $$ x=-2 $$

Use the slope formula to find the slope of the line between (0, -4) and (5, 2).

In the following exercises, graph each equation. $$ y=2 x $$

Do you prefer to graph the equation \(y=\frac{2}{3} x-2\) by plotting points or intercepts? Why?
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Statistics

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.