Section outline

  • Proportional Relationships in Equations
    ::等量中的比例关系

    Y ou will be introduced to the equation of a line. As shown in lesson , lines that pass through the origin have a constant of proportionality , k .   For any proportional relationship ,  k = y x  (such as a line that passes through the origin).  Find the equation of the line by solving for y  in the constant of proportionality equation.
    ::您将被引入线的方程。 如课程所示, 穿过源的线有一定的相称性, k。 对于任何比例关系, k=yx( 如通过源的线) 。 在比例性方程中为 y 找到线的方程 。

    k = y x x ⋅ k = y x ⋅ x k x = y

    ::k=yxxxxx=y=yxxxxx=y

    This equation  y = k x  is another representation of a proportional relationship.
    ::这个公式y=kx 是比例关系的另一个表示 。

    Digital Downloads
    ::数字下载

    A website offers music downloads for $0.79 per song. 
    ::一个网站提供每首歌0.79美元的音乐下载。

    • Use the slider to see how the cost changes as you increase the number of songs you buy.  
      ::使用滑块查看成本如何变化, 当你增加您购买的歌曲数量时 。
    • Use the record button to mark different price points on the table in the interactive. Then use the data you record to answer the questions below.
      ::使用记录按钮来标记互动中表格上的不同价格点。然后使用您记录的数据回答下面的问题。
    INTERACTIVE
    Downloading Digital Songs
    minimize icon
    • Drag the red slider to change the number of songs downloaded and observe how much it costs.
      ::拖曳红色滑块以改变下载的歌曲数量并观察其成本。
    • Press the white button to record up to 3 costs in the table.
      ::按下白色按钮,将最多3个成本记录在表格中。
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    Likes P er Minute
    ::喜欢每分钟

    On a social media site, the number of likes you receive for a recent post are in the table below.
    ::在社交媒体网站上,您最近获得的网友数量见下表。

    minutes 1 5 7 10
    number of likes 3 15 21 30

    Take the values in the table and plot them in the graph. Then, use the graph to determine the constant of proportionality and the equation of the line.
    ::将表格中的值取出并在图表中绘制。然后,使用图表来确定线的相称性和方程的常数。

    INTERACTIVE
    Likes on Social Media
    minimize icon
    • Plot the values from the table above by dragging the red points from the origin to where they belong.
      ::从上表绘制值,将红点从来源拖到所属位置。
    • You can press the Check button to check your work.
      ::您可以按“ 检查” 按钮检查您的工作 。
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    Discussion Question
    ::讨论问题

    A proportional relationship can be represented by a table of values, a graph, and an equation. Discuss how you can find one representation if you are given one of the other two.
    ::比例关系可以用一个数值表、一个图表和一个方程式来表示。讨论如果给您给其它两个中的一个,您如何找到一个表示 。

    for some examples !  
    ::举例来说!

    How are They the Same?
    ::他们如何是相同的?

    You can represent a proportional relationship in different ways. Below is a Venn diagram  with three circles, one for each representation. Drag each of the words, graph, table, and equation to a circle. Then drag the appropriate descriptors to each word to each circle. If something is a property of two or three of the representations, put that descriptor in the one of the overlapping areas.  
    ::您可以以不同的方式代表比例关系。下面是一个Venn图,有三个圆,每个代表符各一个。将每个单词、图表、表格和方程式拖到一个圆上。然后将每个单词的适当描述符拖到每个圆上。如果表示符中有两个或三个的属性,请将该描述符放在重叠区域之一。

    INTERACTIVE
    Proportional Relationship Venn Diagram
    minimize icon
    • Drag the words "Equation", "Table", "Graph" to the lines that label the circles.
      ::将“等式”、“表”、“格”等字拖到标明圆圈的线条上。
    • Next, drag each of the descriptors to the appropriate region of the diagram.
      ::下一步,将每个描述符拖到图表的适当区域。
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    Discussion Questions
    ::讨论问题 讨论问题

    1. Why do you think there are different representations of a proportional relationship?
      ::你觉得为什么比例关系 会有不同的表达方式?
    2. How does your Venn Diagram compare to the Venn diagrams of other students?
      ::你的文恩图如何与其他学生的文恩图相比?

     Summary
    ::摘要

    • The equation that represents a proportional relationship, or a line, is y = k x ,  where k  is the constant of proportionality.
      ::表示比例关系或直线的方程式是 y=kx, k 是比例的常数 。
    • Use k = y x  from either a table or a graph to find k and create the equation.
      ::使用表格或图表中的 k=yx 来查找 k 并创建方程式 。
    • Proportional relationships can be represented by tables, graphs and equations.
      ::比例关系可以用表格、图表和方程式表示。