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Chapter 4: Problem 323

Determine the most convenient method to graph each line. \(x=-3\)

Short Answer

Expert verified
Draw a vertical line through x = -3 on the x-axis.

Step by step solution

01

Identify the Equation Type

Recognize that the equation given is of the form x = constant. This is a vertical line.
02

Set Up the Graph

To graph the line, first, draw the coordinate axes on graph paper.
03

Plot the Line

Since the equation is x = -3, identify the point where x equals -3 on the x-axis. Draw a vertical line through this point. The line should extend infinitely in both directions along the y-axis.
04

Label the Line

Label the line as x = -3 to indicate its equation.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Vertical Lines
A vertical line in a graph is a line that runs up and down, parallel to the y-axis. The equation of a vertical line is always in the form \(x = \text{constant}\). This means that no matter where you are on the line, the value of x remains the same. For example, for the equation \( x = -3 \), every point on this line has an x-coordinate of -3. Unlike other types of lines, the slope of a vertical line is undefined, as it does not move horizontally.
Coordinate Axes
Coordinate axes are the two perpendicular lines on a graph that define the coordinate plane. The horizontal line is called the x-axis and the vertical line is called the y-axis. These lines intersect at a point called the origin, denoted as \( (0, 0) \). When drawing a graph, it is essential to set up the coordinate axes correctly:
  • Draw two perpendicular lines on graph paper, one horizontal and one vertical.
  • Label the horizontal line as the x-axis and the vertical line as the y-axis.
  • Mark the origin where the two axes intersect.
Having these axes allows you to accurately plot and understand points on the graph.
Plotting Points
Plotting points is the process of identifying specific locations on a graph by their coordinates. Each point is represented by an ordered pair \( (x, y) \), where x is the position on the horizontal axis and y is the position on the vertical axis. To plot a point:
  • Start from the origin (0, 0).
  • Move horizontally to the x-coordinate.
  • From there, move vertically to the y-coordinate.
  • Mark the point where these two movements intersect.
In the case of the vertical line \( x = -3 \), you only need to move to -3 on the x-axis and then draw a vertical line through it because the y-coordinate can be any value.
Labeling Graphs
Labeling graphs is crucial for clarity and understanding. When you graph a line or plot points, always indicate what each line and point represents. For the line \( x = -3 \):
  • After drawing the vertical line at \( x = -3 \), write the equation \( x = -3 \) along the line.
  • Label the axes clearly, indicating which is the x-axis and which is the y-axis.
By labeling your graphs, anyone who views them can instantly understand what each element represents, making your graphs informative and easy to interpret.

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Most popular questions from this chapter

Graph the linear inequality \(x+5 y<-5\)

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