1.4 在图表中确定比例关系-interactive

Section outline

• Select section General

  Collapse Expand

  General

  Collapse all Expand all

  • Select activity 新闻通告

    

    新闻通告 Forum
• Select section 确定图表中的比例关系

  Collapse Expand

  确定图表中的比例关系

  播放段落

  Drive Away
  ::开车离开

  播放段落

  Any proportional relationship can be graphed like the two cars in the following interactive. As you may notice, the point values of the cars is also proportional, like the values in the table. This makes sense because the table values are just the  $\begin{align*}x\text{-}\end{align*}$  and $\begin{align*}y\text{-}\end{align*}$ values from each point! A graph is simply another way to represent a proportional relationship.  
  ::任何比例关系都可以像两辆汽车一样在以下交互式中绘制图表。 正如您可能注意到的, 汽车的点值也是比例的, 就像表格中的值一样。 这有道理, 因为表格的值只是每个点的 x 值和 Y 值 。 图表只是代表比例式关系的另一种方式 。

   

   

   

   

  播放段落

  Any proportional relationship can be graphed like the two cars in the interactive. As you may notice, the point values of the cars is also proportional, like the values in the table. This makes sense because the table values are just the $\begin{align*}x\text{-}\end{align*}$  and $\begin{align*}y\text{-}\end{align*}$ values from each point! A graph is simply another way to represent a proportional relationship.  
  ::任何比例关系都可以像互动中的两辆汽车一样图形化。 正如您可能注意到的, 汽车的点值也是比例化的, 和表格中的值一样。 这有道理, 因为表格的值只是每个点的 x 和 Y 值 。 图表只是代表比例化关系的另一种方式 。

   

  ---

  播放段落

  Turkey Time
  ::土耳其时间土耳其时间

  播放段落

  The table below gives the cook times of turkeys depending on their weight at 325°F. 
  ::下表根据火鸡在325°F时的重量,列出火鸡的烹饪时间。

  播放段落

  Drag the turkey in the graph so that it lines up with the values in the table.
  ::在图形中拖动火鸡,使其与表格中的值一致。

  weight (lbs)	10	12	15	18	20
  time (min)	150	180	225

   

   

   

   

  播放段落

  Discussion Question:
  ::讨论问题:

  播放段落

  What do you notice about this graph and the graph of the Driving Away interactive?
  ::你注意到这个图和驾驶式互动的图吗?

  ---

   

  播放段落

  Half Marathon Training
  ::半马拉松训练

  播放段落

  From this interactive, it is important to note that all proportional relationships pass through the origin when graphed . The origin  is the point  $\begin{align*}(0, 0)\end{align*}$  on the graph. It is also the point where the  $\begin{align*}x\text{-}\end{align*}$  and $\begin{align*}y\text{-}\end{align*}$ axes intersect.  We can also conclude that the point $\begin{align*}(1, r)\end{align*}$ represents the unit rate for any proportional relationship. 
  ::从此交互式关系中,必须注意所有比例关系在图形绘制时都通过源。 来源是图形上的点( 0, 0) 。 同时也是 X 和 y 轴交叉点。 我们还可以得出结论, 点(1, r) 代表任何比例关系的单位率 。

  播放段落

  The graph below shows the relationship between time in minutes and the number of miles that Abby runs while training for a half marathon. It takes her 17 minutes to run 2 miles, 42.5 minutes to run 5 miles, and 93.5 minutes to run 11 miles. 
  ::下图显示了时间以分钟计数和Abby在训练半马拉松时跑多少英里之间的关系。 她花了17分钟跑2英里,42.5分钟跑5英里,93.5分钟跑11英里。

  播放段落

  Drag the points on the origin to the three points represented above.
  ::将源点的点拖到上面代表的三点。

   

   

   

   

  播放段落

    Summary
  ::摘要

  播放段落
  • A graph and table can both represent proportional relationships
    ::图表和表格既可以代表比例关系,也可以代表比例关系
  播放段落
  • The graph of a proportional relationship is a line that goes up at a constant rate, and goes through the origin.
    ::比例关系图是一条直线 以恒定速率上升 贯穿源头
  播放段落
  • The point  $\begin{align*}(1, r)\end{align*}$  represents the unit rate of the graph.
    ::点(1,r)代表图形的单位速率。