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  [Figure 1]

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  Casey's family is trying new things on their adventure vacation. Casey is excited about riding a zipline for the very first time. The beginning point is 20 meters higher than the end point, and the length of the zipline is 200 meters. What is the slope of the line?
  ::凯西的家人在冒险度假时正在尝试新的东西。 凯西对第一次骑拉链很兴奋。开始点比终点高20米,而拉链的长度是200米。 什么是线的斜坡?

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  In this concept, you will learn about slopes and how to graph them. 
  ::在这个概念中,你将了解斜坡和如何用图表绘制它们。

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  Slope
  ::斜斜度

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  A  slope  can be defined as the steepness of a straight line. It is the ratio of the change in  vertical  measure to the change in horizontal measure. This is also referred to as the ratio of "rise" to  "run"  or the change in y to the change in x. 
  ::斜坡可以定义为直线的陡度。它是垂直测量变化与水平测量变化之比。这也被称为“ 上升” 与“ 运行” 之比或y 变化与 x 变化之比。

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  The Greek letter Delta,  $\begin{array}{r}\mathrm{\Delta }\end{array}$ , is used to show the changes in x and y.
  ::希腊字母 Delta 用于显示 x 和 y 的更改 。

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  $\begin{array}{r}\mathrm{\Delta }y\end{array}$  stands for the change in y.
  ::你代表你的变化

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  $\begin{array}{r}\mathrm{\Delta }x\end{array}$  stands for the change in x.
  ::x 表示 x 的更改 。

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  Line AB on the  coordinate plane  below has a change of 5 units  vertically ,  $\begin{array}{r}\mathrm{\Delta }y\end{array}$  . 
  ::下面坐标平面上的AB线垂直改变5个单位,YY。

  

  [Figure 2]

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  The slope of line AB is the ratio  $\begin{array}{r}\frac{rise}{run}\end{array}$ or   $\begin{array}{r}\frac{\mathrm{\Delta }y}{\mathrm{\Delta }x}\end{array}$  =  $\begin{array}{r}\frac{5}{6}\end{array}$  .
  ::AB线的斜坡是比率 r i s e r u n 或 y x = 5 6。

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  Line AB, with a slope of  $\begin{array}{r}\frac{5}{6}\end{array}$ , is a  positive slope .The line slants upward from left to right.
  ::AB线,斜坡为5 6,是一个正斜坡。 线向上倾斜,从左向右倾斜。

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  Slopes can be positive or negative. Regardless of the  quadrant , or point values, slopes are based on the change of y (increase or decrease) as the x value moves from left to right.
  ::斜坡可以是正的,也可以是负的。无论象限值或点值如何,随着 x 值从左向右移动,斜坡以y(增加或减少)的变化为基础。

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  A line that slants up from left to right has a  positive slope.
  ::从左向右倾斜的线有一个正斜坡。

  

  [Figure 3]

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  A line that slants down from left to right has a  negative slope .
  ::从左向右倾斜的线有负斜坡。

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  Horizontal and vertical lines also have a slope. A horizontal line has a change in x, but it does not have a change in y.
  ::水平线和垂直线也有一个斜坡。水平线在 x 中有变化,但在 y 没有变化。

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  slope =  $\begin{array}{r}\frac{\mathrm{\Delta }y}{\mathrm{\Delta }x}\end{array}$  =  $\begin{array}{r}\frac{0}{\mathrm{\Delta }x}\end{array}$  = 0
  ::斜坡 = y y x = 0 x = 0

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  The slope of a horizontal line is 0.
  ::水平线的斜坡是 0 。

  

  [Figure 4]

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  A vertical line has a change in y, but it does not have a change in x.
  ::垂直线对 y 有变化, 但对 x 没有变化 。

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  slope =  $\begin{array}{r}\frac{\mathrm{\Delta }y}{\mathrm{\Delta }x}\end{array}$  =  $\begin{array}{r}\frac{\mathrm{\Delta }y}{0}\end{array}$ =  undefined
  ::斜度 = y x = y 0 = 未定义

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  Division  by zero is undefined.
  ::未定义除以 0 的除法 。

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  The slope of a vertical line is undefined.
  ::垂直线的斜坡没有定义。

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  Examples
  ::实例

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  Example 1
  ::例1

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  Earlier, you were given a problem about Casey and the zip line.
  ::早些时候,你得到一个问题 凯西和拉链线的问题。

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  The change in elevation, vertical  distance , was 20m, and the change in horizontal distance was 200m. What is the slope?
  ::高度变化,垂直距离是20米,水平距离变化是200米。斜坡是什么?

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  First, write the  equation .
  ::首先,写出方程式

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  slope =  $\begin{array}{r}\frac{\mathrm{\Delta }y}{\mathrm{\Delta }x}\end{array}$
  ::斜坡 = y x

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  Next,  substitute  in the given values. 
  ::其次,在给定值中替换。

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    $\begin{array}{r}\frac{\mathrm{\Delta }y}{\mathrm{\Delta }x}=\frac{20}{200}\end{array}$
  ::y y x = 20 200

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  Then, reduce.
  ::然后,减少。

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  The answer is that the slope equals  $\begin{array}{r}\frac{1}{10}\end{array}$
  ::答案是斜坡等于110

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  Example 2
  ::例2

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  Determine if the slope of the line below is positive or negative. What is its value?
  ::确定下线的斜坡是正的还是负的。 其值是多少 ?

  

  [Figure 5]

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  First, determine if the line rises or falls as it moves from left to right.
  ::首先,确定直线在从左向右移动时是上升还是下降。

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  The line falls as it moves from left to right. The slope is negative.
  ::线在从左向右移动时跌落。 斜坡为负 。

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  Next, use the equation to find the value of the slope.
  ::接下来,使用方程来找到斜坡的值。

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  slope =  $\begin{array}{r}\frac{\mathrm{\Delta }y}{\mathrm{\Delta }x}\end{array}$  
  ::斜坡 = y x

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   total change in y = -8 units
  ::y = -8 单位总变化 y = - 8 单位

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  total change in x = 6 units
  ::x = 6 单位总变化数

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    $\begin{array}{r}\frac{\mathrm{\Delta }y}{\mathrm{\Delta }x}=\frac{\text{-}8}{6}\end{array}$
  ::y y x = - 8 6

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   Then, reduce to lowest  terms .
  ::然后,降低到最低值。

  $\begin{array}{r}\frac{\text{-}8}{6}=\text{-}1.33\end{array}$

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  Next, remember that the slope is negative.
  ::接下来,请记住斜坡是负的。

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  The answer is the slope equals  $\begin{array}{r}-1.33\end{array}$  
  ::答案是斜坡等于-1.33。

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  Example 3
  ::例3

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  Determine the slope:
  ::确定斜坡 :

  

  [Figure 6]

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  First, determine if the slope is positive or negative.
  ::首先,确定斜坡是正的还是负的。

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  The line rises as it moves from left to right. The slope is positive.
  ::线条从左向右移动时会上升。 斜坡是正向的 。

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  Next, use the  formula .
  ::下一个,使用公式。

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  slope =   $\begin{array}{r}\frac{\mathrm{\Delta }y}{\mathrm{\Delta }x}\end{array}$  =  $\begin{array}{r}\frac{2}{7}\end{array}$  
  ::斜坡 = y y x = 2 7

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  The answer is the slope equals  $\begin{array}{r}\frac{2}{7}\end{array}$
  ::答案是斜坡等于2 7

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  Example 4
  ::例4

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  Identify the slope of each line shown below.
  ::标明以下每一行的坡度。

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  1. 

     [Figure 7]
     
     ::[图7]
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  2.  
     

     [Figure 8]
     
     ::[表8]

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  First, consider the line in  $\begin{array}{r}a\end{array}$ .
  ::首先,考虑一下这条线。

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  The line is vertical.
  ::这条线是垂直的。

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  Next, remember that a vertical line has a slope that is undefined.
  ::下一步, 请记住垂直线有一个未定义的斜坡 。

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  The answer is that the slope of line a is undefined.
  ::答案是线a的斜坡没有定义。

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  Then, consider the line in  $\begin{array}{r}b\end{array}$ .
  ::然后考虑B中的线条。

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  The line is horizontal.
  ::线是水平的。

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  Next, remember that a horizontal line has a slope equal to zero.
  ::下一步,请记住水平线的斜度等于零。

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  The answer is that the slope of line b equals 0.
  ::答案是,b线的斜坡等于0。

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  Example 5
  ::例5

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  Murray broke his arm and could not use the rope to climb into his treehouse. Instead, he got a ladder from the garage and set it up against the structure. The treehouse is 15 feet off the ground, and Murray set it 3 feet away from the side. What is the slope of the ladder? Is it positive or negative?
  ::Murray断了胳膊,不能用绳子爬进他的树屋。相反,他从车库里拿到了梯子,把它固定在结构上。树屋离地面15英尺,Murray把梯子离侧3英尺。梯子的斜坡是正的还是负的?

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  First write the formula.
  ::先写公式

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  slope =  $\begin{array}{r}\frac{\mathrm{\Delta }y}{\mathrm{\Delta }x}\end{array}$
  ::斜坡 = y x

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  Next, substitute in what is known. 
  ::接下来, 取代已知的东西。

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  $\begin{array}{r}\frac{\mathrm{\Delta }y}{\mathrm{\Delta }x}=\frac{15}{3}\end{array}$
  ::y y x = 15 3

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  Then, reduce to lowest terms.
  ::然后,降低到最低值。

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  The answer is that the slope equals 5. 
  ::答案是斜坡等于5

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  Whether the slope is positive or negative can only be determined if there is a diagram or graphing coordinates given.
  ::斜坡是正的还是负的,只有在给出图表或图形坐标时才能确定。

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  Review
  ::回顾

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  For each graph, tell if the slope of the line shown is positive, negative, zero, or undefined.
  ::对于每个图表,请说明显示的线的斜度是正、负、零或未定义的。

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  1. 

     [Figure 9]
     
     ::[图9]
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  2. 

     [Figure 10]
     
     ::[图10]
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  3. 

     [Figure 11]
     
     ::[表11]
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  4. 

     [Figure 12]
     
     ::[图12]
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  5. 

     [Figure 13]
     
     ::[图13]
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  6. 

     [Figure 14]
     
     ::[表14]
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  7. 

     [Figure 15]
     
     ::[图15]
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  8. 

     [Figure 16]
     
     ::[图16]
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  9. 

     [Figure 17]
     
     ::[图17]
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  10. 

      [Figure 18]
      
      ::[图18]

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  Answer each question.
  ::回答每个问题。

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  11. Does a positive slope have to contain positive numbers?
      ::一个正斜坡是否必须包含正数?
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  12. True or false. A horizontal line is undefined.
      ::真实的或虚假的。 水平线未定义 。
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  13. True or false. A negative slope goes down from right to left.
      ::阴性斜坡从右向左倾斜
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  14. True or false. A vertical line has an undefined slope.
      ::垂直线有一个未定义的斜坡。
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  15. True or false. You can figure out any slope as long as the line has some slant to it.
      ::你可以找出任何斜坡 只要线偏向于斜坡

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  Review (Answers)
  ::回顾(答复)

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  Click   to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
  ::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键 。

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  Resources
  ::资源