1.3 确定表格中的比例关系-interactive

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• 选择节确定表格中的比例关系

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  确定表格中的比例关系

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  Coffee House Spending
  ::咖啡厅开支

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  Your math teacher has a serious coffee habit. Every morning she goes to her favorite coffee house and buys a latte for $3.75. Here is a table to represent how much money she spends in a week:
  ::你的数学老师有一个严重的咖啡习惯。每天早上她去她最喜欢的咖啡屋, 买杯拿铁3.75美元。这里是一张表,用来代表她一周花多少钱:

  Money	$3.75	$7.50
  Days	1	2	3	4	5

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  • Determine the total for days 3, 4 and 5 and create a ratio of money to days. 
    ::确定第3、4和5天的总数,并设定货币与日之比。
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  • Use the sliders to adjust the numerator to be the money amounts and the denominator to represent the days. 
    ::使用滑动符将分子调整为货币金额和代表天数的分母。

   

  

  INTERACTIVE

  Coffee House Spending

  

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  • Use the sliders to adjust the numerator which represents money amounts and the denominator which represents days.
    ::使用滑动符调整代表金额的分子和代表天数的分母。
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  • Numbers shown are rounded to the hundredths place.
    ::显示的数字四舍五入到千位。

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  Determine how much money your math teacher spent on lattes on day 3 of the week.
  ::确定你的数学老师 每周第3天在拿铁上花多少钱

  a

  $3.75

  b

  $7.50

  c

  $11.25

  d

  $15.00

  Hint

   

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  The table in this interactive is an example of a proportional relationship . All the ratios you set up were equal. These are also known as equivalent ratios . If your break this down into  its key components, you will see that :
  ::此交互式表格中的表格是比例关系的一个示例。 您设置的所有比率都是相等的。 这些比率也被称为等值比率。 如果您将其细分为关键组成部分, 您将会看到 :

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  • A proportion is an equation that sets equivalent ratios equal to each other. All of these rates create a proportion because they are in a proportional relationship.
    ::比例是一个等式,它规定等同比率对等,所有这些比率都形成一个比例,因为它们是比例关系。
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  • $3.75 is the rate of change . It describes how fast the output (the total cost) increases each day.
    ::3.75美元是变化率,说明产出(总成本)每天增长的速度。
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  • The rate of change is always constant (or same) for any proportional relationship.
    ::任何比例关系的变化率总是不变(或相同)。

   

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  Painting the House
  ::画房子

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  Max is painting his house. He needs to cover 3,200 square feet of wall space. Based on the table below, how many gallons of paint does Max need to buy?
  ::他需要覆盖3200平方英尺的墙壁空间。根据下面的表格, Max需要买多少加仑的油漆?

  gallons	1	2	3	4	5
  square feet	400	800	1,200	1,600	2,000

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  Use the sliders to change the proportions and determine how many gallons of paint are needed.
  ::使用滑块来改变比例,并确定需要多少加仑油漆。

   

  

  INTERACTIVE

  Painting the House

  

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  • Use the sliders to change the proportions and determine how many gallons of paint Max needs to buy.
    ::使用滑块来改变比例 并确定需要买多少加仑的油漆 Max.
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  • Numbers shown are rounded to the hundredths place.
    ::显示的数字四舍五入到千位。

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  The rate of change of a proportional relationship is also called the constant of proportionality because for every rate , the proportion of  $\begin{array}{r}\frac{\text{dependent value}}{\text{independent value}}\end{array}$  is constant. This constant of proportionality is commonly labeled $\begin{array}{r}k.\end{array}$   T he independent value, usually labeled x, is often in the first column of a table. The dependent value, which is usually labeled y, is commonly the second column of a table. Therefore , you can say:
  ::比例关系的变化率也称为相称性不变值,因为对于每一比率,依赖性价值的比重是不变的。这一相称性不变值通常被贴上标签 k。独立值通常被贴上标签 x,通常在表格第一列中。依赖性值通常被贴上标签 y,通常是表格第二列。因此,你可以说:

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  $$\begin{array}{r}\frac{\text{dependent value}}{\text{independent value}}=\frac{y}{x}=k\end{array}$$

  
  ::独立值=yx=k

   

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  Is it Proportional?
  ::是相称的吗?

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  Determine if the following tables represent proportional relationships. If so, find the constant of proportionality and the equation. 
  ::确定下列表格是否代表比例关系。如果是,请找到相称性和等式的常数。

   

  

  INTERACTIVE

  Is It Proportional?

  

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  • Click on the all the tables that have proportional  $x$  and  $y$  values.
    ::单击所有有比例 x 和 y 值的表格。

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     Summary
  ::摘要

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  • Tables can be used to determine whether or not data is proportional.
    ::可用表格确定数据是否成比例。
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  • Proportional relationships have a constant rate of change or constant of proportionality, called  $\begin{array}{r}k.\end{array}$
    ::比例关系有不变的变化率或相称性不变,称为k。
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  • You can use  $\begin{array}{r}k\end{array}$  to find other values within the proportional relationship.
    ::您可以使用 k 在比例关系中找到其它值 。