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Chapter 9: Problem 26

Determine the intercepts and graph each linear equation. $$y=2$$

Short Answer

Expert verified
The y-intercept is (0, 2), and there is no x-intercept. Graph is a horizontal line at y = 2.

Step by step solution

01

Identify the equation

The given linear equation is \( y = 2 \).
02

Determine the y-intercept

For the equation \( y = 2 \), the y-intercept is the value of \( y \) when \( x = 0 \). Here, \( y \) is always 2, so the y-intercept is \((0, 2)\).
03

Determine the x-intercept

To find the x-intercept, set \( y = 0 \) and solve for \( x \). However, since \( y = 2 \) is a constant and never equals 0, there is no x-intercept.
04

Graph the equation

To graph \( y = 2 \), draw a horizontal line that passes through the point \((0, 2)\). This line extends infinitely in both the positive and negative x-directions but stays constant at \( y = 2 \).

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Key Concepts

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

Understanding the Y-Intercept
The y-intercept is a key concept when graphing linear equations. It is the point where the line crosses the y-axis. In simpler terms, it's the value of y when x is 0.
For example, in the linear equation given in the exercise, \[ y = 2 \], the y-intercept is determined as follows:
  • We observe the equation \[ y = 2 \]
  • Here, y is always 2, regardless of the value of x
  • Therefore, the y-intercept is \((0, 2)\).
To summarize: The y-intercept tells us where the line crosses the y-axis, and in this case, it's at the point \((0, 2)\).

Exploring the X-Intercept
The x-intercept is another important concept in graphing. This is where the line crosses the x-axis, meaning it's the value of x when y is 0.
Let's check out our example with the equation \[ y = 2 \]:
  • To find the x-intercept, we set \[ y = 0 \] and solve for x
  • But, in the equation \[ y = 2 \], y is always 2 and never 0
  • This means there is no x-intercept for this equation
So, in our example with \[ y = 2 \], there is no point where the line crosses the x-axis because y is always 2.

Graphing a Horizontal Line
When a linear equation is of the form \[ y = c \], it represents a horizontal line. Here, 'c' is a constant.
For instance, in the equation given, \[ y = 2 \]:
  • This means that y is always 2, regardless of x's value
  • To graph this, we draw a horizontal line that crosses the y-axis at \((0, 2)\)
  • This line extends infinitely in both the positive and negative x-directions but remains constant at \[ y = 2 \]
A horizontal line isn't affected by the value of x. It simply means y maintains a constant value along the entire line.

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Most popular questions from this chapter

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