4.9 与阴性窗一起工作-interactive

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  How Nurses Use Math
  ::护士如何使用数学

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  This section will explore negative slopes and their meaning. The field in which you will explore this is nursing. Mathematics is extremely important in the nursing field. Nurses must convert medicine dosages, understand a patient’s vital signs, operate a drip machine, and much more. As a nurse, mathematical accuracy is important to the health of their patients. This is why every nurse must pass a test to ensure that they can perform the required calculations without making mistakes. In this section, you will look at  the math behind operating a drip machine.
  ::本节将探讨负斜坡及其含义。 您要探讨的领域是护理。 数学在护理领域极为重要。 护士必须转换药物剂量,了解病人的生命迹象,操作滴滴机,等等。 作为护士,数学精确度对其病人的健康很重要。 这就是为什么每个护士都必须通过测试,以确保他们能够进行所需的计算而不会犯错误。 在本节中,你将观察开滴机背后的数学。

   

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  Negative Slopes
  ::负负缩

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  Before you explore how a drip machine works, you must first understand negative slopes.  You have seen positive slopes that rise from left to right. This represents a quantity that is increasing by a constant amount. A negative slope represents a quantity that is decreasing by a constant amount. Use the interactive below to explore negative slopes.
  ::在探索滴滴机如何工作之前, 您必须首先了解负斜坡。 您已经看到正斜坡从左向右上升。 这表示一个数量正在以恒定数量增长。 负斜坡代表一个数量正在递减一个恒定数量。 使用下面的互动来探索负斜坡 。

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  To find a negative slope, you will take the same approach that you did for finding a positive slope . C ount the number of steps to get from one point to another. Begin by finding the slope in the image below:
  ::要找到一个负斜坡, 您将采取与找到正斜坡相同的方法。 计算从一个点到另一个点的步数。 从在下面的图像中找到斜坡开始 :

  

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   To get from point A to point B, you need to take one step down and two steps to the right.
  ::要从A点到B点,你必须往下一步,向右两步。

   

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  The  slope equals  $\begin{align*}-\frac{1}{2}.\end{align*}$
  ::斜坡等于 -12

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  When calculating a slope, the negative may appear in the numerator or the denominator.  A negative slope is typically written with the negative in front of the fraction .
  ::当计算斜坡时,负数可能出现在分子或分母中。负数斜坡通常在分数前面写为负数。

  $$\begin{align*}-\frac{13}{8} = \frac{-13}{8} = \frac{13}{-8}\end{align*}$$

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  Discussion Question
  ::讨论问题

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  1. How could $\begin{align*}\frac{−13}{8}\end{align*}$   and $\begin{align*}\frac{13}{−8}\end{align*}$   affect how you move from one point to another in different directions? How can slopes that take you in different directions be used to represent the same line?
     ::-138 和 13-8 如何影响您如何从一个点向另一个点向不同方向移动? 如何用向不同方向移动的斜坡来代表同一行?
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  2. Why is $\begin{align*}-\frac{13}{8}\end{align*}$   not equal to $\begin{align*}\frac{-13}{-8}?\end{align*}$  
     ::为什么-138不等于-13-8?

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  Use the interactive below to practice finding positive and negative slopes.
  ::使用下面的交互方式来练习寻找正斜坡和负斜坡。

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  Discussion Question
  ::讨论问题

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  What are some situations that a negative slope could represent?
  ::消极坡度代表哪些情况?

   

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  How Nurses Use Math Continued
  ::护士如何继续使用数学

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  Nurses use drip machines to administer medicine to a patient slowly. They begin with a large quantity of medicine, and the drip machine sends the medicine to the patient one drip at a time. One example of when a nurse might have to use a drip machine is when a patient is dehydrated. Dehydration can be caused by not drinking enough water or from an illness. It is important to stay hydrated by drinking enough water, especially during the summer months and during times of increased physical activity. To treat a patient suffering from dehydration, a nurse will use a drip machine to administer Saline, which helps increase hydration in the body.
  ::护士使用滴水机向病人缓慢地提供药品,从大量药品开始,滴水机一次将药品送给病人一次滴水。护士可能必须使用滴水机的一个例子是病人脱水,脱水可能是由于水不足或疾病造成的;必须保持水分充水,特别是在夏季几个月和身体活动增加的时候;为治疗脱水病人,护士将使用滴水机管理盐碱,这有助于增加身体的水分。

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  Example
  ::示例示例示例示例

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  A nurse must give a patient 1500 mL, which holds approximately 22,500 drops, of Saline at a rate of 30 drops per minute. Graph the linear relationship that shows the volume Saline that is left, measured in drops, over time.
  ::护士必须给病人1500毫升的盐碱,它大约保持22 500滴,每分钟30滴。 绘制线性关系图,显示盐碱的剩余体积,用下降量衡量,随时间推移。

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  To graph this relationship, use the slope-intercept form of $\begin{align*}y = mx + b. \end{align*}$  The $\begin{align*}y\text{-}\end{align*}$ intercept , $\begin{align*}b, \end{align*}$ represents the starting amount which is 22,500 drops. The slope represents the rate at which the quantity is changing which is 30 drops per minute. Since the amount of saline in the machine is decreasing, the slope will be -30.  You can put this into the equation to obtain the following:
  ::要绘制此关系图, 请使用 y =mx+b 的斜坡界面。 y 界面, b, 表示起始量为 22 500 下方。 斜度表示数量变化的速度, 每分钟30 下方。 由于机器中的盐碱量正在下降, 斜度将是 - 30 。 您可以将此项放入方程, 以获得以下结果 :

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  $$\begin{align*}y = -30m + 22,500\end{align*}$$
  ::y30米+22 500

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  Use the interactive below to explore how this rate changes over time.
  ::使用下面的交互方式来探讨这一比率如何随时间推移而变化。

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  Discussion Question
  ::讨论问题

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  Where on the graph will the medicine run out? At what time will this happen?
  ::药要用到哪里?

    

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  Cell  Phone Battery Life
  ::手机电池生命

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  P ractice graphing a linear equation in slope-intercept form that has a negative slope.
  ::练习用斜坡拦截形式绘制线性方程图,该方程为负斜坡。

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  Example
  ::示例示例示例示例

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  The battery on a phone starts at 100%. Every hour, the battery decreases by 2.5% points. Write and graph an equation which will show the phones battery life over time.
  ::手机上的电池以100%的速度启动。 每小时, 电池会减少2.5% 点。 写入并绘制一个方程式, 该方程式将显示电话电池的寿命 。

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  To write this as an equation, use slope-intercept form of $\begin{align*}y = mx + b. \end{align*}$  The variable $\begin{align*}x\end{align*}$  will represent the time in hours, and the variable y will represent the battery life of the phone. The $\begin{align*}y\text{-}\end{align*}$ intercept, $\begin{align*}b, \end{align*}$  represents the starting amount which is 100. The slope represents the rate at which the quantity is changing which is 2.5 percentage points per hour. Since the battery life is decreasing, the slope will be -2.5.  You can write this as an improper fraction to help find the rise and the run. The decimal 2.5 can be written as the mixed number  $\begin{align*}2\tfrac{1}{2}.\end{align*}$   You can then convert this to the improper fraction  $\begin{align*}\tfrac{5}{2}.\end{align*}$   Putting this into the equation , you obtain the following:
  ::要将此写成一个方程, 请使用 y=mx+b 的斜度界面。 变量 x 将代表小时时间, 变量 y 将代表电话的电池寿命。 y 界面, b 代表起始量为 100 。 斜度代表数量变化的速度, 变化速度为每小时2.5 百分点。 由于电池寿命正在下降, 斜度将是 - 2. 5 。 您可以将此写成一个不适当的分数来帮助查找上升和运行。 小数 2.5 可以写成混合数 212 。 然后您可以将其转换为不适当的分数 52 。 把这个分数放进方程, 您可以得到以下信息 :

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  $$\begin{align*}y = -\frac{5}{2} x + 100\end{align*}$$
  ::y52x+100

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  U se the slope and $\begin{align*}y\text{-}\end{align*}$ intercept to graph the linear equation using the interactive below.
  ::使用斜坡和 Y 界面用下面的交互方程绘制线性方程图。

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  Discussion Question
  ::讨论问题

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  1. What does the $\begin{align*}y\text{-}\end{align*}$ intercept represent in the context of the problem?
     ::y-inter概念在问题的背景中代表什么?
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  2. What does the $\begin{align*}x\text{-}\end{align*}$ intercept represent in the context of the problem?
     ::在问题的背景中, X 界面代表什么?

   

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     Summary
  ::摘要

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  • A negative slope represents a quantity that is decreasing by a constant amount.
    ::负斜坡代表不断减少的数量。
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  • A negative slope can have a negative r ise and a positive r un   or a positive r ise and negative r un.
    ::负斜坡可能出现负上升和正回升,或正回升和负回升。