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Chapter 2: Problem 75

Find an equation of each line. Horizontal line through \((12, -62)\)

Short Answer

Expert verified
The equation is \( y = -62 \).

Step by step solution

01

Understand the Concept of a Horizontal Line

A horizontal line goes straight across from left to right. The slope of such a line is zero because it does not rise or fall as it moves horizontally.
02

Identify the Equation Format

The equation of a horizontal line can be written as \(y = c\), where \(c\) is the y-coordinate of any point on the line.
03

Extract the Necessary Information

Identify the y-coordinate of the given point \( (12, -62) \), which is \(-62\).
04

Form the Equation

Using the y-coordinate \(-62\), the equation of the horizontal line is \( y = -62 \).

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Key Concepts

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

slope
Understanding the slope is crucial when working with different types of lines. The slope represents the steepness or incline of a line. It is calculated as the ratio of the vertical change (rise) to the horizontal change (run). However, for a horizontal line, there is no vertical change. This means the rise is zero. Since the rise is zero, the slope of a horizontal line is always zero. This is why horizontal lines appear flat, moving straight from left to right without any incline. Understanding the zero slope helps us identify the specific equation format for horizontal lines.
y-coordinate
The y-coordinate of a point tells us how far up or down the point is on the Cartesian plane. In the case of the horizontal line, the y-coordinate remains constant. This means every point on the line has the same y-coordinate. In our example, the point given is \(12, -62\). Here, \(-62\) is the y-coordinate. No matter the value of *x*, the y-coordinate will always be \(-62\) because the line is horizontally aligned. This constant y-coordinate is key to forming the equation of the line.
equation format
The equation format for horizontal lines is straightforward. Since the slope is zero and the y-coordinate is consistent, the equation of any horizontal line is written as \(y = c\). The \(c\) in this format represents the constant y-coordinate. For the example given, the y-coordinate of the point is \(-62\), making the equation of the horizontal line \(y = -62\). This format emphasizes that for any value of \(x\), the y-coordinate remains the same, thus forming a horizontal line.

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Most popular questions from this chapter

Find the domain of the function given by each equation. $$ g(x)=\frac{1}{2 x} $$

Determine whether each equation is linear. Find the slope of any nonvertical lines. $$ 2 y-30=0 $$

Find the intercepts. Then graph by using the intercepts, if possible, and a third point as a check. $$ g(x)=2 x-9 $$

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