Problem 86 - Introductory and Intermediate Algebra for College Students 4th

Question

Describe the graph of \(x=-100\).

Step-by-Step Solution

Answer

The graph of the equation \(x = -100\) is a vertical line located at point -100 on the x-axis.

Step 1: Identify the type of line

The equation \(x = -100\) represents a vertical line because it has a fixed x value across all points on the line.

Step 2: Determining the location of the line

As the equation states that \(x = -100\), it means that the vertical line is located 100 units left from the origin point, on the x-axis.

Step 3: Draw the line

Draw a vertical straight line on the point (-100, 0), extending it both ends upward and downward. This line represents the graph of the equation \(x = -100\).

Key Concepts

Graphing Equations

Graphing equations involves taking an equation and visualizing it on a coordinate plane. For instance, linear equations such as \(x = -100\) create straight lines. When you graph an equation, you start by understanding the equation itself. What does it represent?

• A vertical line is represented by an equation where \(x\) is equal to a constant value.
• All points on this line have the same \(x\)-coordinate.

In the case of \(x = -100\), it means every point on the line has an \(x\)-coordinate of -100. This makes it a vertical line that doesn’t change in the \(x\) direction. This is distinct from horizontal lines, which have constant \(y\)-coordinates.
Understanding how to translate equations into lines and shapes on a graph is a foundational skill in mathematics, making concepts more tangible. Consider practicing with different types of equations to see how lines are formed.

Coordinate Plane

The coordinate plane is a two-dimensional surface where we graph equations. It consists of two intersecting lines: the horizontal line called the x-axis, and the vertical line called the y-axis. These lines meet at a point called the origin, written as \((0, 0)\), and separate the plane into four quadrants. Each quadrant helps in identifying the position and direction of lines.
You can think of the coordinate plane as a giant piece of graph paper.

• The x-axis runs left to right, indicating horizontal movement.
• The y-axis runs up and down, indicating vertical movement.

When plotting points or lines, each point is identified by an ordered pair \((x, y)\) that shows where the point is located relative to the axes. This system makes it easy to plot and identify specific points and the relationships between them.

X-axis

The x-axis is an essential part of the coordinate plane. It’s the horizontal axis that plays a crucial role in graphing equations. When plotting any point or line, the x-coordinate tells you how far to move left or right from the origin.

• If \(x\) is positive, move right.
• If \(x\) is negative, move left.

For instance, in the equation \(x = -100\), the x-coordinate of every point on the line is -100. This fact places the line 100 units to the left of the origin on the x-axis, illustrating how critical the x-axis is in determining position.
Understanding the x-axis is key in navigating the coordinate plane, helping to accurately locate and draw both points and lines. It lays the groundwork for more complex graphing concepts and allows for effective spatial visualization in math problems.