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Chapter 5: Problem 8

Graph the equation. $$ x=7 $$

Short Answer

Expert verified
Answer: The equation \(x=7\) represents a vertical line when graphed on a Cartesian coordinate system, and it intersects the x-axis at the point (7, 0).

Step by step solution

01

Set up coordinate system

Set up a Cartesian coordinate system (x-axis and y-axis) and mark some points on each axis. Make sure to label the axes with "x" and "y".
02

Identify the equation

The given equation is \(x = 7\). This means that for any point on this line, the x-coordinate will always be 7, and the y-coordinate can be any value.
03

Plot the points on the graph

Plot several points on the graph where the x-coordinate is 7, and the y-coordinate can vary. For example, plot the points (7, -2), (7, 0), (7, 2), and (7, 4).
04

Connect the points

Connect all the plotted points with a straight line. This represents the equation \(x=7\). The line should be vertical and pass through the x-axis at x=7.
05

Label the line

Label the line as \(x=7\) to show that it represents the given equation. Now, the graph of the equation \(x=7\) is complete.

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Key Concepts

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

Understanding the X-Axis and Y-Axis
In a Cartesian coordinate system, the x-axis and y-axis are essential elements that serve as reference lines for plotting points on a graph. These two axes are perpendicular to each other and intersect at the origin, which has the coordinates (0, 0).
  • The x-axis runs horizontally and is usually drawn from left to right. It is labeled with positive numbers extending to the right and negative numbers extending to the left.

  • The y-axis runs vertically, extending upward with positive numbers and downward with negative numbers.

  • By labeling the x-axis with "x" and the y-axis with "y," we establish a clear framework for identifying locations on the graph.

This system allows us to represent relationships between two variables in a visual manner. The understanding of these axes forms the foundation for graphing equations such as the vertical line in an exercise like ours.
Plotting Points on Graph
Plotting points on a graph involves marking a location where two values, one from each axis, intersect. This process is fundamental to graphing equations. Let's explore it in simple steps:
  • First, identify the x-coordinate, which tells you how far along the x-axis the point is located.

  • Next, identify the y-coordinate to determine how far along the y-axis the point is positioned.

  • Given a point, for example (7, -2), start at the origin, move 7 units along the x-axis, and then move down to -2 on the y-axis.

  • Mark the point where these two positions meet on the graph.

In the case of the equation \(x = 7\), all points share the same x-coordinate of 7, meaning each point will be directly aligned vertically along this line.
The Concept of a Vertical Line
A vertical line is a straight line parallel to the y-axis, and it is defined by an equation where the x-value is constant, like \(x=7\) in our exercise.
  • Unlike horizontal lines, which can be described by an equation \(y = c\) (where "c" is a constant), vertical lines maintain a constant x-value.

  • This means that regardless of the y-coordinate, the line will always pass through the same x-coordinate.

  • To visualize this, imagine a string pulled tight up and down through \(x=7\) on the graph. Every y-coordinate value corresponds to this same vertical line.

  • As such, points like (7, -2), (7, 0), (7, 2), and so on, lie directly on the line.

Grasping the concept of vertical lines is crucial for correctly plotting and understanding certain types of linear equations that show fixed x-values and varying y-values.

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Most popular questions from this chapter

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