调查水平线和垂直线

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What Do Horizontal and Vertical Lines Mean?
::水平线和垂直线意味着什么?

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Horizontal and vertical are two special cases of linear relationships. Horizontal lines are lines that run directly from left to right and are parallel to the $\begin{array}{r}x\text{-}\end{array}$ axis. Vertical lines are lines that run directly up and down and are parallel to the $\begin{array}{r}y\text{-}\end{array}$ axis. In this section, you will explore these types of lines in detail and learn how they are used in everyday life. Use the interactive below to examine these linear relationships and their equations.
::水平线和垂直线是线性关系的两个特殊实例。 水平线是直接从左向右运行的直线, 与 X 轴平行。 垂直线是直接上下运行的直线, 与 y 轴平行。 在本节中, 您将详细探索这些类型的线, 并了解这些类型的线在日常生活中是如何使用的。 使用下面的交互式线性来检查这些线性关系及其等式 。

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Discussion Questions
::讨论问题 讨论问题

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1. Set the graph to the equation y=2. What is the of this equation? What is the y-intercept ?
   ::将图形设置为 y=2 方程。 这个方程是什么? y 界面是什么 ?
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2. Set the graph to the equation x=3. What is the slope of this equation? What is the y-intercept?
   ::将图形设置为方程式 x=3 。 这个方程式的斜度是多少? y 界面是什么 ?
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3. Discuss with a classmate how we can use our knowledge that the x-axis and y-axis are perpendicular to each other to prove that horizontal and vertical lines are perpendicular to each other? Do you agree with your classmate, why or why not?
   ::与同学讨论我们如何利用我们的知识来证明 X 轴 和 y 轴 相互垂直 , 以证明水平线和垂直线相互垂直 。 您是否同意您的同学的意见, 为什么或为什么不同意 ?

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Horizontal Lines
::水平线

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Of the two special types of linear relationships discussed in this chapter, horizontal lines are the most commonly seen. Horizontal lines are used to represent a constant with no changing rate . To understand this , revisit the babysitting example that you have been using, but this time you will change the rate.
::在本章讨论的两种特殊类型的线性关系中,最常看到的是水平线。水平线用于代表一个不变的、没有变化的速率。要理解这一点,请重温您一直在使用的保姆示例,但这次您将更改速率。

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Example
::示例示例示例示例

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Emily has recently begun babysitting for family and friends to earn money. She charges a flat rate of $20. What would this look like on a graph? What equation would be used to model this situation?
::Emily最近开始照看家人和朋友赚钱。她收取20美元的固定费率。在图表上,这看起来像什么?用什么方程式来模拟这种情况?

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To understand this, consider the possibilities where Emily works 1 hour, 2 hours and 3 hours. To do this, you will make a table.
::为了理解这一点,请考虑艾米丽工作1小时2小时3小时的可能性。要做到这一点,你将做一个桌子。

Hours Worked	Money Earned ($)
1	20
2	20
3	20

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Regardless of how many hours Emily’s babysitting session lasts, she will make $20. If you graph this, you will get the following: 
::无论Emily的保姆课程持续了多少小时,她都会赚20美元。如果你用图表来显示这一点,你会得到以下信息:

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An equation that reflects a flat rate is a flat line with a slope of 0. This graph shows that, in this case, the cost will always be $20. W rite the equation for a horizontal line as  $\begin{array}{r}y=c\end{array}$   where the variable $\begin{array}{r}c\end{array}$  is the constant. A horizontal line will always pass through the point $\begin{array}{r}(0,c)\end{array}$  on the $\begin{array}{r}y\text{-}\end{array}$ axis and will run parallel to the $\begin{array}{r}x\text{-}\end{array}$ axis.
::反映统一费率的方程式是斜度为 0 的平面线。 此图显示, 在此情况下, 成本总是 20 美元。 将水平线的方程式写成 y=c , 变量 c 是 常数 。 水平线总是通过 Y 轴上的点 (0, c) , 并将与 x 轴平行运行 。

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Discussion Question
::讨论问题

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1. What would the slope of this equation be?
   ::这个等式的斜坡是什么?
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2. Discuss with a classmate what would the slope of all horizontal line equations be 0? Why or why not?
   ::与同学讨论,所有水平线方程式的斜坡是0?为什么或为什么不是?

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Example
::示例示例示例示例

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A video store wants to keep track of how many movies they sell. They want to start keeping track of the month starting with the 200 movies they have already sold. The month went by they didn't sell any movies! Create a graph to show how many movies they sold through the month starting with the 200 they already sold. What does the graph tell you?
::一个视频商店想要追踪他们卖了多少部电影。 他们想要开始跟踪这个月的纪录, 从他们已经卖了200部电影开始。 月过去了他们没有卖任何电影! 创建一个图表来显示他们卖了多少部电影, 从他们卖了200部开始的这个月。 图表告诉你什么?

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This graph shows that the store had sold 200 movies, but through the next 30 days, they didn't sell any movies!
::这张图显示,这家商店卖了200部电影, 但是在接下来的30天里, 他们没有卖任何电影!

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Vertical Lines
::垂直直线

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Vertical line equations may be less commonly seen than horizontal equations but they pop up in a variety of places. The most common use for vertical lines is in computing, where they can be used to model an object that runs straight up and down. They can also be used to represent a situation with one desirable option. In fact, you saw these equations in Linear Equations  without even realizing it. Anytime you got an answer like $\begin{array}{r}x=3\end{array}$ , you secretly had a vertical line. It isn’t until a situation involves two variables that you see it expressed on a coordinate plane .
::垂直线方程式可能比水平方程式更不常见,但它们会在不同的地方弹出。 垂直线方程式最常用的用途是计算, 它可以用来模拟一个直向上向下运行的物体。 它们也可以用来代表一个可取的选项。 事实上, 您在线性方程式中看到这些方程式时甚至没有意识到它。 每当您得到一个像 x=3 这样的答案时, 您就会暗中有一个垂直线条。 直到一个情况涉及到在坐标平面上表达的两个变量时, 您才会看到它 。

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Example
::示例示例示例示例

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John  is building a shelf for a closet. The closet is 3 feet wide so the shelf will have to be 3 feet wide. There is no restriction on length. Graph the relationship between width and length.
::约翰正在为壁橱建一个架子。 壁橱宽3英尺, 使架子宽3英尺。 长度没有限制。 绘制宽度和长度之间的关系图 。

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Our only restriction is that the closet has to be 3 feet wide.  U se $\begin{array}{r}x\end{array}$  to represent the width and  $\begin{array}{r}y\end{array}$  to represent the length. B egin by filling out the table below to examine possible combinations:
::我们唯一的限制是壁橱必须宽3英尺。 使用 x 表示宽度, y 表示长度。 首先填写下表以检查可能的组合 :

Width (x)	Length
3	1
3	2
3	3

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When you graph this table, you obtain the following:
::绘制此表格时,可获取以下信息:

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This graph shows that the width will always be 3 feet and that it may not depend on the length, a concept you will explore further in chapter 7. Write the equation for a vertical line as  $\begin{array}{r}x=c\end{array}$  where the variable c is the constant. A vertical line will always pass through the point $\begin{array}{r}(c,0)\end{array}$  on the $\begin{array}{r}x\text{-}\end{array}$ axis and will run parallel to the $\begin{array}{r}y\text{-}\end{array}$ axis.
::此图显示宽度将始终为 3 英尺, 且不取决于长度, 您将在第 7 章中进一步探讨这个概念。 将垂直线的方程写成 x=c , 变量 c 是常数。 垂直线将总是通过 x 轴上的点( c, 0) , 并会与 y 轴平行运行 。

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Discussion Questions
::讨论问题 讨论问题

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1. What would the slope of this equation be?
   ::这个等式的斜坡是什么?
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2. Discuss with a class would the slope of all vertical line equations be undefined ? Do you agree with your classmate? Why or why not?
   ::与某类讨论, 所有垂直线方程式的斜坡是否都未定义 ? 您是否同意同学的意见 ? 为什么或为什么不?

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Example
::示例示例示例示例

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Megan wants to compare how many books she has read to how many pages she has read. So far, she is on page 237 in her first book, what would the graph of this look like if the number of pages read is on the x-axis?
::梅根想比较她读过多少本书和读过多少页。 到目前为止,她在第一本书的第237页上,如果读过多少页是在x轴上,这个图会是什么样子?

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The graph shows that Megan has read over 200 pages in one book.
::该图显示Megan在一本书中读了200多页。

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Writing Equations for Horizontal and Vertical Lines
::水平线和垂直线的书写公式

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You can use the knowledge from graphing horizontal and vertical equations to write equations for them. The trick is to write “the axis it goes through = the number it goes through”. If a horizontal line passes through the $\begin{array}{r}y\text{-}\end{array}$ axis at 5 you would write $\begin{array}{r}y=5.\end{array}$  If a vertical line passes through the $\begin{array}{r}x\text{-}\end{array}$ axis at -2 you would write $\begin{array}{r}x=-2.\end{array}$  
::您可以使用水平和垂直方程式的图形化知识为其写入方程式。 关键是写入“ 轴通过 = 数字通过 ” 。 如果一条水平线在 5 点通过 y 轴, 您可以写 y = 5 。 如果一条垂直线在 - 2 点通过 x 轴, 您可以写 x = 2 。

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Use the interactive to practice identifying the equation of a given horizontal or vertical line. 
::使用互动方式练习确定某一水平或垂直线的方程。

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Discussion Questions
::讨论问题 讨论问题

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1. Where would $\begin{array}{r}x=0\end{array}$  be placed?
   ::x=0将放置在哪里?
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2. Where would $\begin{array}{r}y=0\end{array}$  be placed?
   ::将你的位置放在哪里?