4.5 解释 Y 界面和斜坡-interactive

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  解释 Y 界面和斜体

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  Firefighters Continued
  ::消防员 继续

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  T he  lesson     discussed how firefighters choose hose pressure using a linear relationship but did not  show the entire picture. The starting pressure of the hose when pointing directly forward at the first floor is 130 psi (pounds per square inch - a measure of pressure). For every floor off of the ground, a firefighter needs to add 5 psi to the hose.  When they are putting out a fire on the second floor, firefighters will increase the pressure to 135 psi. In this section, you will be exploring this linear relationship, and others like it, in more detail.  You will be looking at two important features of linear relationships: and y-intercept .
  ::该课讨论了消防员如何使用线性关系选择软管压力,但没有展示整个图象。当直接指向一楼时,软管的起始压力是130 psi(每平方英寸磅-压力度)。对于地面的每层楼,消防员需要在水管上加5 psi。当消防员在二楼放火时,消防员将把压力提高到135 psi。在本节中,你们将探索这一线性关系,以及其他类似关系。你们将研究线性关系的两个重要特征:y 和 y 界面。

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  Discussion Question
  ::讨论问题

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  What would the pressure need to be set to for a fire on the 5th floor of a building?
  ::大楼五楼发生火灾需要承受什么压力?

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  Determining Hose PSI
  ::确定Hose PSI

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  When a firefighter is fighting a fire with a hose, the pressure in the hose starts 130 pounds per square inch  and must increase by 5 psi for every additional floor off the ground. A ssume that the ground floor is floor 1. Use the interactive below to explore how this linear relationship would look in a table and on a graph.
  ::当消防员用水管扑灭火时,水管的压力每平方英寸130磅,每增加一层地面必须增加5皮西。假设地面是1层,用下面的交互作用来探讨这种线性关系在一张桌子和一张图上会如何看。

  

  INTERACTIVE

  Determining Hose PSI

  

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  • Drag the slider to set the pressure of water in the hose in pounds per square inch (PSI) to put out the fire.
    ::拖动滑动器,将水管中的水压以每平方英寸磅计,以扑灭大火。
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  • Press "Extinguish" to put out the fire.
    ::按"出口"来灭火
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  • Press "Reset" to find a new fire to extinguish.
    ::按“ 重置” 键以寻找要熄灭的新火焰 。
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  • Click "Table" to see the relationship between psi and the floor reached by the fire fighter.
    ::点击“表”查看Psi和消防员到达的地板之间的关系。

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  The slope of the line representing the relationship between PSI and the floor reached by the firefighter is @$\begin{align*}\frac{1}{5}\end{align*}@$ .
  ::代表 PSI 与消防员所到达的楼层之间关系的线的斜坡是 @$\ begin{ alignfrac{ 1\ @ 5{ end{ align} $ 。

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  Remember that slope is expressed as a fraction in the form @$\begin{align*}\tfrac{\text{rise}}{\text{run}}.\end{align*}@$
  ::记住, 斜度以窗体表示为分数@$\ begin{ align} tfrac\ text{ rise{ text{ run}\.\end{ align} $ 。

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  TRUE
  ::真实

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  FALSE
  ::公平交易

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  Discussion Questions
  ::讨论问题 讨论问题

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  1. Discuss with a classmate what the y-intercept represents in the context of the situation.
     ::与同学讨论y-inter概念在形势下代表什么。
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  2. Discuss with a classmate what the slope represents in the context of the situation.
     ::与同学讨论斜坡在局势中代表什么。
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  3. Does where the firefighter stands matter in this scenario? Discuss with a classmate what values might change if the firefighter stands farther away or closer to the building.
     ::与同学讨论,如果消防员离大楼更远或更近,什么价值会改变。

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  Understanding the Y-intercept
  ::理解 Y 界面

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  S lope is the steepness of a line. The y-intercept is the point where the line crosses the $\begin{array}{r}y\text{-}\end{array}$ axis. This point often represents the starting amount. Use the interactive below to practice identifying the $\begin{array}{r}y\text{-}\end{array}$ intercept .  
  ::斜坡是线的陡度。 y 截取是线横跨 y 轴的点。 此点通常代表起始值。 使用下面的交互作用来练习识别 y 截取 。

  

  INTERACTIVE

  What is the y-intercept?

  

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  • Input the coordinates of the  $y-$ intercept into the input boxes.
    ::输入框输入 y - 界面的坐标。
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  • If you get the correct answer, you can try again with a new line.
    ::如果您得到正确的答案, 您可以用新的线再次尝试 。

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  Discussion Questions
  ::讨论问题 讨论问题

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  1. What did the coordinates of each of the y-intercepts have in common?
     ::每个 Y 界面的坐标有什么共同点?
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  2. Why is the x-coordinate always 0?
     ::为什么x坐标总是0?
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  3. Is it possible for a line to cross not cross the y-axis ?
     ::一条线能否越过Y轴线?

     

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  Rigid Motions in Linear Relationships
  ::线性关系中的硬性动议

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  When you change the slope and $\begin{array}{r}y\text{-}\end{array}$ intercept of a linear relationship, you are performing a rigid motion on the line. Use the interactive below to explore how changing the slope and $\begin{array}{r}y\text{-}\end{array}$ intercept affect the line formed by a linear equation .
  ::当您改变线性关系的斜坡和 Y 界面时,您正在对线性关系进行僵硬的动作。使用下面的交互动作来探索如何改变斜坡和Y 界面对线性方程形成的线条产生影响。

  

  INTERACTIVE

  Y intercept and Slope

  

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  • Move the sliders to see how the y-intercept and slope changes.
    ::移动滑动器以查看 Y 界面和斜坡是如何变化的 。

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  Summary
  ::摘要

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  • The y-intercept is the point at which the line crosses the y-axis, and is defined as the point (0,y).
    ::y 界面是线横跨 y 轴的点,被定义为点 (0,y)。
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  • In a linear relationship, the slope represents the relationship between the two variables  $\begin{array}{r}x\end{array}$ and $\begin{array}{r}y.\end{array}$
    ::在线性关系中,斜坡代表两个变量Xandy之间的关系。
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  • The greater the slope, the steeper the line will be.
    ::斜坡越大,斜线越陡。