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Chapter 1: Problem 15

Find an equation of the given line. Horizontal through \((2,9)\)

Short Answer

Expert verified
y = 9.

Step by step solution

01

Understand Horizontal Lines

A horizontal line has a constant y-value, meaning it does not change as x changes. The general equation of a horizontal line is in the form of y = c, where c is the y-coordinate through which the line passes.
02

Identify the Y-Value

From the given point (2, 9), identify the y-coordinate. In this case, the y-coordinate is 9.
03

Write the Equation

Using the y-coordinate identified in Step 2, write the equation of the line in the form y = c. Here, the equation will be y = 9.

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Key Concepts

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

horizontal lines
Understanding horizontal lines is crucial when dealing with coordinate geometry. A horizontal line runs parallel to the x-axis and has a constant y-value. This means no matter where you are on this line, the y-coordinate remains unchanged. Consequently, the equation of any horizontal line can be written in the form of \(y = c\), where \(c\) is the value of the y-coordinate.

In simpler terms, imagine a perfectly straight line running right to left across your graph paper. If you were to place a dot anywhere on this line, it would always have the same vertical position.
y-coordinate
The y-coordinate is a key component when plotting points in a Cartesian coordinate system. In an ordered pair \((x, y)\), \(y\) represents the vertical position of a point relative to the x-axis. When dealing with horizontal lines, identifying the correct y-coordinate is essential.

For instance, in the point \(2, 9\), the y-coordinate is 9. So, if a line passes through this point and is horizontal, then every point on this line will share this same y-coordinate of 9. Thus, regardless of the x-value, the line's equation will always be \(y = 9\).
linear equations
Linear equations form the foundation of understanding lines in mathematics. A linear equation typically represents a straight line when graphed. The most common forms are:
  • Standard form \(Ax + By = C\)
  • Slope-intercept form \(y = mx + b\)
  • Vertical lines \(x = k\)
  • Horizontal lines \(y = c\)
When the slope \(m\) is zero, the equation simplifies, representing a horizontal line. Here, \(y = c \), where \(c\) is the y-coordinate of every point on that line.

Understanding these different forms helps in recognizing and writing the equation for different types of lines with ease.

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Most popular questions from this chapter

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