比例关系图解解图

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Proportional Relationships in Art
::艺术中的比例关系

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In this lesson, you will be working with the graphs of proportional relationships. You will practice finding the constant of proportionality and interpreting points within a real-world context. Constructing a graph of proportional relationships goes a long way towards understanding them.
::在此教训中, 您将使用比例关系图。 您将练习在现实世界中找到比例和解释点的常态。 构建比例关系图将大大帮助您理解它们 。

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Proportional relationships are vital to artists when trying to recreate a person or object. If the proportions of the figure are not correct then the painting or sculpture will look strange. Find the constant of proportionality between your arm length and your total height.
::比例关系对于艺术家在试图重建某个人或对象时至关重要。 如果数字比例不正确, 则绘画或雕塑会显得奇怪 。 找到您的手臂长度和总高度之间的比例性常数 。

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Discussion Questions:
::讨论问题:

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1. Write the equation $\begin{array}{r}y=kx\end{array}$   where $\begin{array}{r}x\end{array}$   is the total height, $\begin{array}{r}y\end{array}$   is arm length and $\begin{array}{r}k\end{array}$   is the constant of proportionality.
   ::写入公式 y=kx, x 是总高度, y 是平长, k 是相称性的常数 。
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2. Construct a graph using 5 points from the relationship in question 1.
   ::构造一个图形, 使用问题1中关系5点的图形 。
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3. Leonardo uses the equation $\begin{array}{r}y=0.45x,\end{array}$   from which the point $\begin{array}{r}(15,6.75)\end{array}$   is obtained. How could this point be useful to an artist? How could this equation be useful to an artist?
   ::Leonardo使用y=0.45x的方程式,从中取出点(15,6.75),这对艺术家有什么用?这个方程式对艺术家有什么用?

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Filling the Sandbox
::填满沙箱

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Example
::示例示例示例示例

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Santiago is filling a sandbox for his little brother. The dimensions of the sandbox are $\begin{array}{r}8\text{ft}\times 8\text{ft}\times 6\text{in. }\end{array}$ The graph below shows the relationship between the volume of the sandbox and number of pounds of sand. How much sand does he need to fill the entire box?
::圣地亚哥正在为他弟弟填沙箱。 沙箱的尺寸是8ftx8ftx6in。 下图显示了沙箱的体积和沙磅数量之间的关系。 他需要多少沙子才能填满整箱?

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• Find the volume of the sandbox, in feet.  You will need to convert the depth (6 inches) in to feet. Volume is $\begin{array}{r}\text{length}\times \text{width}\times \text{depth}\end{array}$ .
  ::查找沙箱的体积, 以足为单位。 您需要将深度( 6英寸) 转换为脚。 体积是长度xwidthx 深度 。
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• Determine the constant of proportionality from the graph.
  ::从图表中确定相称性的常数。
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• Use $\begin{array}{r}k\end{array}$  to determine how many pounds of sand he needs.
  ::用K来确定他需要多少磅沙子

 

 

 

 

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Discussion Question
::讨论问题

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Are there different ways to determine if a point is on a line? List as many different ways as you can.
::是否有不同的方法来确定点是否在线上? 尽可能多地列出不同的方式 。

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how to find a point on a line for help!
::如何在线上找到求救的点!

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Recall, in order to find the unit rate from a graph, the point $\begin{array}{r}(1,r)\end{array}$  is used. When finding the constant of proportionality from a graph, you can also use this point, but only the $\begin{array}{r}y\text{-}\end{array}$ value is equal to  $\begin{array}{r}k.\end{array}$  In addition , any point on the line (except the origin) can be used to find $\begin{array}{r}k,\end{array}$  using the ratio  $\begin{array}{r}\frac{y}{x}.\end{array}$  Then, you can plug in your $\begin{array}{r}k\end{array}$  value to the equation  $\begin{array}{r}y=kx.\end{array}$
::回想时,为了从图表中找到单位率,将使用点(1,r)。在从图表中找到相称性常数时,您也可以使用此点,但只有 Y 值等于 k。此外,线上的任何点(来源除外)都可以使用 yx 来查找 k。然后,您可以将 k 值插入公式 y=kx 中。

 

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App-ealing Advertisements
::招贴广告

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You may notice that on some free apps there is advertising, which is used to cover the cost of developing it. Annoy U Advertising offers app developers $1.00 for every 15 people that click on their ad. Ad-Vice Advertising offers developers $1.00 for every 20 clicks.
::您可能会注意到,在一些免费应用程序上,有广告,用来支付开发成本。 Anoy U广告每15个点击自己的广告的人就提供1美元。 Ad-fivile广告每20个点击就提供1美元。

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Using the graph, plot the two lines, find their equations, and determine which deal is better for the app developers.  
::使用此图, 绘制两条线, 找到它们的方程, 并确定哪些交易对应用程序开发者更好 。

 

 

 

 

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When graphing proportional relationships, it is important to be able to create a graph based on data from both a table or an equation. The table is easy; plot the points in the table as $\begin{array}{r}(x,y)\end{array}$  and connect them. If you are given an equation, plot (0, 0) and then a second point $\begin{array}{r}(x,y)\end{array}$  that satisfies the equation. For example, if the equation is  $\begin{array}{r}y=2x,\end{array}$  plot (0, 0) and (1, 2) because  $\begin{array}{r}2=2(1).\end{array}$
::当绘制比例关系时,必须能够根据表格或方程式中的数据创建图表。表格很简单;将表格中的点标为(x,y)并连接它们。如果给您给定一个方程式,绘图(0,0),然后是满足方程式的第二个点(x,y)。例如,如果方程式是 y=2x,绘图(0,0)和绘图(1,2),因为 2=2(1)。