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Chapter 11: Problem 108

In the following exercises, graph each equation. $$ y=5 $$

Short Answer

Expert verified
Draw a horizontal line through the point (0, 5).

Step by step solution

01

Identify the Equation

The given equation is a horizontal line represented by the equation: \( y = 5 \).
02

Understand the Equation

Realize that for any value of \( x \), the value of \( y \) is always \( 5 \). Thus, the line is horizontal and crosses the y-axis at 5.
03

Plot the Y-Intercept

On a graph, mark the point where the line crosses the y-axis. Here it is at the point (0, 5).
04

Draw the Horizontal Line

Draw a straight horizontal line through the point (0, 5) on the graph. This line extends infinitely in both directions along the x-axis.

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Key Concepts

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

plotting y-intercept
The y-intercept is the point where a line crosses the y-axis. For the equation \( y = 5 \), the y-intercept is located at the point (0, 5). To plot the y-intercept on a graph, do the following:

  • First, find the y-axis on your graph.
  • Next, locate the value '5' on the y-axis.
  • Then, mark a point at (0, 5). This is your y-intercept.
The point (0, 5) is crucial because it helps you to understand where the line starts on the y-axis. This point will be used to draw the complete horizontal line.
understanding horizontal lines
Horizontal lines have a very specific characteristic: they are flat and parallel to the x-axis. This means the value of \( y \) remains constant, and the equation can be written as \( y = c \), where \( c \) is any constant. For our exercise, the line is \( y = 5 \). Here are some important points to understand:

  • For any value of \( x \), \( y \) will always be 5.
  • Horizontal lines always have a slope of 0 because there is no rise as you move along the line.
  • These lines stretch infinitely in both the left and right directions.
Knowing these properties helps in identifying and graphing horizontal lines more easily.
graphing linear equations
Graphing linear equations involves plotting points and then connecting them to form a straight line. Let's talk about the basics of graphing a simple linear equation like \( y = 5 \):

  • Identify the type of line by the equation. In this case, \( y = 5 \) tells us it is a horizontal line.
  • Find the y-intercept, which is provided directly in the equation. Here, it is the point (0, 5).
  • Plot this y-intercept on a graph.
  • Draw a straight horizontal line through this point, extending infinitely in both directions along the x-axis.
When plotting other linear equations, you might have different forms, like \( y = mx + b \) (slope-intercept form), which gives more information about the slope and y-intercept. But the process of identifying, plotting, and drawing remains quite similar.

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