1.5 单位比率和比例性常数-interactive

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  单位比率和比例性常数

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  Constant of Proportionality
  ::相 均 度 常 常 数

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  A unit rate is the rate of change in a relationship where the rate is per 1 .
  ::A单位费率是每1人中比率为每1人中某一关系的变化率。

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  The rate of change is the ratio between the  $\begin{array}{r}x\end{array}$  and  $\begin{array}{r}y\end{array}$  (or input and output) values in a relationship .  Another term for the rate of change for proportional relationships is the constant of proportionality . If the rate of change is  $\begin{array}{r}\frac{y}{x},\end{array}$  then so is the constant of proportionality.  To simplify things, we set   $\begin{array}{r}\frac{y}{x}=k,\end{array}$  where $\begin{array}{r}k\end{array}$  represents the constant of proportionality. 
  ::变化率是关系中的 x 和 y (或输入和输出) 值之间的比率。 比例关系中变化率的另一个术语是比例的常数。 如果变化率是 yx ,那么比例的常数就是 yx 。 为了简化事物, 我们设置了 yx=k, K 代表比例的常数 。

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  If you solve a  $\begin{array}{r}\frac{y}{x}=k\end{array}$   equation for  $\begin{array}{r}y,\end{array}$  (like this:  $\begin{array}{r}y=kx\end{array}$ ), it is called a equation. In a direct variation equation, $\begin{array}{r}y\end{array}$  varies directly with $\begin{array}{r}x.\end{array}$  When $\begin{array}{r}x\end{array}$  increases or decreases, $\begin{array}{r}y\end{array}$  also increases or decreases by the same proportion .  To find $\begin{array}{r}y\end{array}$  in a direct variation equation, multiply $\begin{array}{r}x\end{array}$  by the constant of proportionality,  $\begin{array}{r}k\end{array}$ .
  ::如果您为 y 解决 Y y yx=k 方程式( 类似 : y=kx) , 它就被称为 公式。 在直接变异方程式中, y 与 x 直接变化。 当 x 增加或减少时, y 也以相同比例增减。 要在直接变异方程式中找到 y, 乘 x 成正比值, k 。

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  • For example:  Given  the  relationship $\begin{array}{r}y=7x,\end{array}$  the constant of proportionality  $\begin{array}{r}k=7,\end{array}$   so  if $\begin{array}{r}x=3,\end{array}$   then  $\begin{array}{r}y=3\times 7\end{array}$  or $\begin{array}{r}21.\end{array}$
    
    ::例如:根据关系y=7x, 相称性常数k=7, 所以 ifx=3, 然后y=3x7 或 21。
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  • Given the same relationship, if $\begin{array}{r}x=7,\end{array}$   then $\begin{array}{r}y=7\times 7\end{array}$ , or $\begin{array}{r}49.\end{array}$  
    ::如果 x=7, 那么y=7x7, 或者49, 相同的关系 。

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  Buying Frozen Yogurt
  ::购买冷冻酸奶

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  Elise and Lupe  went  to their favorite frozen yogurt place, Yogurtdale, which measures the yogurt by weight. Elise's yogurt cost $4.50 and weighed 9 oz , Lupe's yogurt was $3.50 and 7 oz.  
  ::Elise和Lupe去了他们最喜欢的冻酸奶地方,Yogurtdale用重量测量酸奶。Elise的酸奶成本为4.50美元,重量为9oz,Lupe的酸奶为3.50美元和7oz。

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  • Use the sliders on the graph to determine the unit rate for the cost of the yogurt per ounce.
    ::使用图上的滑块来确定每盎司酸奶成本的单位费率。
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  • Find the constant of proportionality for the proportional relationship.
    ::找到比例关系相称性的常数。

  

  INTERACTIVE

  Buying Frozen Yogurt

  

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  • Drag the red points to plot the weight and cost of Elise's and Lupe's yogurt.
    ::拖着红点绘制艾莉丝和鲁佩酸奶的重量和成本

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  It is important to note that are always written with units, and the constant of proportionality $\begin{array}{r}(k)\end{array}$  is not. A comparison of two rates can make a unit rate. A consistently repeating a unit rate makes a constant of proportionality.
  ::必须指出的是,总是用单位写成,而相称性(k)是不变的。 比较两种比率可以得出单位比率。 单位比率的不断重复使比例性不变。

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  Discussion Question
  ::讨论问题

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  Jamal comes to the conclusion that the unit rate and the constant of proportionality are the same thing. Do you agree with Jamal or disagree? How are are the constant of proportionality and the unit rate of a relationship similar and how are they different?
  ::Jamal的结论是,单位比率和相称性不变是一回事。你同意还是不同意Jamal? 相称性不变和关系单位比率如何相似? 两者有何不同?

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  for some examples to help answer these questions!
  ::举例来帮助回答这些问题!

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  Finding k
  ::查找 k

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  There are several graphs and tables below and different values for  $\begin{array}{r}k.\end{array}$
  ::下面有几个图表和表格,k则有不同的数值。

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  Match the constant of proportionality with its graph or table by selecting the value for  $\begin{array}{r}k\end{array}$  that correlates to the values given in the table or graph.
  ::通过选择与表格或图表中给出的数值相关的 k 值,使相称性常数与其图表或表格匹配。

  

  INTERACTIVE

  Finding k

  

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  • Click the white buttons to match the table or graph to the corresponding  $k$   value.
    ::单击白色按钮,使表格或图表与相应的 k 值相匹配。

  
  

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  It is very important to remember that a straight line through the origin means that there is a proportional relationship, and the values in the table (or graph) can be written as  $\begin{array}{r}\frac{y}{x}\end{array}$  to find the constant of proportionality. 
  ::必须记住,通过原产地的直线意味着存在比例关系,表格(或图表)中的数值可以以yx形式写成,以找到成比例的常数。

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  In this last activity , you will use $\begin{array}{r}k\end{array}$  to find other values in a proportional relationship.
  ::在最后一个活动中,您将使用 k 在比例关系中找到其他值 。

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  Bike Trip
  ::自行车旅行

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  The graph below shows the graph of two cyclists who started at the same place and traveled for one hour.
  ::下图显示两位骑自行车的车手的图表,他们从同一地点出发,旅行了一个小时。

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  • Determine how long it takes each cyclist to ride a mile if the purple cyclist rides 18 miles in an hour and the green cyclist rides 20 miles.
    ::如果紫色自行车手每小时骑18英里 绿色自行车手每小时骑20英里
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  • Determine  $\begin{array}{r}k\end{array}$  for each cyclist.
    ::为每个骑自行车者确定 k。
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  • Determine which cyclist is riding faster.
    ::确定哪个骑自行车的人骑得更快

  

  INTERACTIVE

  Bike Riding

  

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  • Press the white button to see how far two bikes travel in 60 minutes.
    ::按下白色按钮,看两辆自行车60分钟内行驶多远。

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     Summary
  ::摘要

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  • A graph with a straight line through the origin represents a proportional relationship.
    ::以直线横穿来源的图表表示比例关系。
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  • A table of values that make equivalent ratios also represents a proportional relationship.
    ::得出等值比率的数值表也代表比例关系。
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  • When the relationship between the values in the graph or table are constant,  $\begin{array}{r}\frac{y}{x}=k.\end{array}$  
    ::当图形或表格中的数值为常数时, yx=k。