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Chapter 0: Problem 10

Graph the following equations. $$x=-4$$

Short Answer

Expert verified
Draw a vertical line through x = -4.

Step by step solution

01

Identify the Type of Equation

The given equation is in the form of x = constant. This is the equation of a vertical line.
02

Determine the Line's Position

The equation given is x = -4. This means that the vertical line will cross the x-axis at -4.
03

Draw the Coordinate Axes

Draw the x-axis (horizontal) and y-axis (vertical) on a graph. Label the axes properly.
04

Plot the Line

Starting at x = -4 on the x-axis, draw a vertical line that goes through all values of y. This line remains at x = -4 for any y coordinate.
05

Label the Graph

Make sure to label the vertical line with the equation x = -4 to make it clear which equation is graphed.

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Key Concepts

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

Vertical Line
A vertical line in Cartesian coordinates is a straight line that moves up and down, parallel to the y-axis. Unlike other lines with varying slopes, vertical lines have an undefined slope. This is because the change in x-coordinates (horizontal difference) is zero, and division by zero is undefined. In equations, a vertical line is represented as \(x = a\), where \(a\) is the x-coordinate where the line crosses the x-axis. For example, the equation \(x = -4\) describes a vertical line that intersects the x-axis at -4.
Coordinate Axes
When graphing linear equations, understanding the coordinate axes is crucial. The coordinate system consists of two perpendicular lines called axes.
  • The x-axis runs horizontally and represents all possible values of x.
  • The y-axis runs vertically and represents all possible values of y.
The point of intersection where these axes meet is called the origin, denoted as \(0,0\). Each axis is divided into positive and negative parts. Positive x-values are to the right of the origin, while negative x-values are to the left. Similarly, positive y-values are above the origin, and negative y-values are below.
Plotting Points
To graph linear equations, you often need to plot points first. Plotting points involves placing them on the graph where their coordinates indicate.
To plot a point like \(x = -4\):
  • Start at the origin \(0,0\).
  • Move horizontally along the x-axis to -4.
  • Since it's a vertical line, it will stretch infinitely in both the upward and downward direction, covering all possible y-values.
This helps in accurately drawing the line according to the given linear equation's format. Properly plotting points is the foundation to ensure the graph representation aligns with the equation's attributes.

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Most popular questions from this chapter

Evaluate \(f(4)\). $$f(x)=x^{0}$$

Find the zeros of the function. (Use the specified viewing window.) $$f(x)=\sqrt{x+2}-x+2 ;[-2,7] \text { by }[-2,4]$$

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Let \(f(x)=\sqrt[3]{x}\) and \(g(x)=\frac{1}{x^{2}} .\) Calculate the following functions. Take \(x > 0\). $$f(g(x))$$

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