课程： 2.6 斜坡-截取表的直线图

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选择节斜坡- 截取窗体中的图形线

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斜坡- 截取窗体中的图形线
The cost per month for a cell-phone plan is $60 plus $7.50 for every gigabyte (GB) of data you use. (For billing purposes, actual usage is rounded to the nearest one-quarter GB.) Write an equation for the cost of the data plan and determine how much your bill will be if you use 4.5 GB of data in a month.

Graphing a Line in Slope Intercept Form
::以斜坡截取窗体绘制线形图

Recall that the equation of a line is $\begin{aligned} y = m x + b \end{aligned}$ , where $\begin{aligned} m \end{aligned}$ is the and $\begin{aligned} b \end{aligned}$ is the $\begin{aligned} y - \end{aligned}$ intercept . From these two pieces of information we can graph any line.
::回顾一行的方程式是 y=mx+b, 其中 m 是 y- interview 和 b 是 y- interview。从这两条信息中, 我们可以绘制任何一行。

Let's graph the following equations.
::让我们用图表来说明以下的方程式。

Graph $\begin{aligned} y = \frac{1}{3} x + 4 \end{aligned}$ on the Cartesian plane .
::笛卡尔飞机上的图y=13x+4。

First, the Cartesian plane is the $\begin{aligned} x - y \end{aligned}$ plane. Typically, when graphing lines, draw each axis from -10 to 10. To graph this line, you need to find the slope and $\begin{aligned} y - \end{aligned}$ intercept. By looking at the equation, $\begin{aligned} \frac{1}{3} \end{aligned}$ is the slope and 4, or (0, 4), is the $\begin{aligned} y - \end{aligned}$ intercept. To start graphing this line, plot the $\begin{aligned} y - \end{aligned}$ intercept on the $\begin{aligned} y - \end{aligned}$ axis.
::首先, 笛卡尔平面是 x - y 平面。典型的情况是, 当绘制图形时, 将每个轴从 - 10 绘制为 - 10 到 10 。要绘制此直线, 您需要找到斜度和 y- interview 。通过查看方程式, 13 是斜度, 4 (0 4) 是 y- interview 。要绘制此直线图, 请在 y- 轴上绘制 y- interview 。

Now we need to use the slope to find the next point on the line. Recall that the slope is also $\begin{aligned} \frac{r i s e}{r u n} \end{aligned}$ , so for $\begin{aligned} \frac{1}{3} \end{aligned}$ , we will rise 1 and run 3 from the $\begin{aligned} y - \end{aligned}$ intercept. Do this a couple of times to get at least three points.
::现在我们需要使用斜坡来找到线上的下一点。回顾斜坡也上升了, 所以对于13, 我们将从 y- intercut 上升1, 从 y- intercut 运行 3 。做一次这样的事情至少要达到 3 个点。

Now that we have three points, connect them to form the line $\begin{aligned} y = \frac{1}{3} x + 4. \end{aligned}$
::现在,我们有三个点, 将它们连接成 y=13x+4 的线条。

Graph $\begin{aligned} y = - 4 x - 5. \end{aligned}$
::图y4x-5。

Now that the slope is negative, the vertical distance will “fall” instead of rise. Also, because the slope is a whole number, we need to put it over 1. Therefore , for a slope of -4, the line will fall 4 and run 1 OR rise 4 and run backward 1. Start at the $\begin{aligned} y - \end{aligned}$ intercept, and then use the slope to find a few more points.
::斜坡是负的, 垂直距离会“ 下降 ” 而不是上升。另外, 由于斜坡是一个整数, 我们需要将斜坡加到 1 上。因此, 对于 4 的斜坡, 线将下降 4 , 运行 1 OR 上升 4 , 向后。从 y - intercut 开始, 然后用斜坡来找到更多的点。

Graph $\begin{aligned} x = 5 \end{aligned}$ .
::图x=5。

Any line in the form $\begin{aligned} x = a \end{aligned}$ is a vertical line. To graph any vertical line, plot the value, in this case 5, on the $\begin{aligned} x - \end{aligned}$ axis. Then draw the vertical line.
::窗体 x=a 中的任何一条线都是垂直线。要绘制任何垂直线,请在 x- 轴线上绘制值,在此情况下为 5。然后绘制垂直线。

To graph a horizontal line, $\begin{aligned} y = b \end{aligned}$ , it will be the same process, but plot the value given on the $\begin{aligned} y - \end{aligned}$ axis and draw a horizontal line.
::要绘制水平线, y=b, 将会是相同的进程, 但绘制在 y- 轴上给定的值, 并绘制水平线。

Examples
::实例

Example 1
::例1

Earlier, you were asked to write an equation for the cost of a data plan, and determine how much your bill will be if you use 4.5 GB of data a month.
::早些时候,你被要求写一个计算数据计划成本的方程式, 并确定如果每月使用4.5GB的数据,你的账单会有多少。

If x is the number of GB of data you use in a month and y is the total cost you pay, then the equation for the cell-phone plan would be $\begin{aligned} y = 7.5 x + 60 \end{aligned}$ . If you use 4.5 GB in a month, the total cost would be $\begin{aligned} y = 7.5 (4.5) + 60 = 93.75 \end{aligned}$ .
::如果 x 是您在一个月中使用的 GB 数据数, y 是您支付的总费用, 那么手机计划的方程式是 y= 7. 5x+60。如果您在一个月中使用4.5 GB, 则总费用是 y= 7. 5 (4.5)+60=93.75。

So your bill for the month would be $93.75.
::所以你这个月的帐单是93.75美元

Example 2
::例2

Graph the following lines.
::绘制下行图。

$\begin{aligned} y = - x + 2 \end{aligned}$ (Plot (0, 2) and the slope is -1, which means you fall 1 and run 1)
::yx+2( 绘图 (0, 2) , 斜度是 - 1, 表示您跌落 1 并运行 1)

$\begin{aligned} y = \frac{3}{4} x - 1 \end{aligned}$ (Plot (0, -1) and then rise 3 and run 4 to the next point, (4, 2))
::y=34x- 1 (绘图( 0, - 1) , 然后上升 3 , 运行 4 到下一点, (4, 2) )

$\begin{aligned} y = - 6 \end{aligned}$ (Plot -6 on the $\begin{aligned} y - \end{aligned}$ axis and draw a horizontal line)
::y6 (在 y- 轴上绘制 - 6 并绘制水平线)

All answers are on the same grid below.
::所有答案都在下面相同的网格上。

Review
::回顾

Graph the following lines in the Cartesian plane.
::在笛卡尔飞机上图解如下行。

$\begin{aligned} y = - 2 x - 3 \end{aligned}$
::y2x-3

$\begin{aligned} y = x + 4 \end{aligned}$
::y=x+4 y=x+4

$\begin{aligned} y = \frac{1}{3} x - 1 \end{aligned}$
::y=13x-1

$\begin{aligned} y = 9 \end{aligned}$
::y=9 y=9

$\begin{aligned} y = - \frac{2}{5} x + 7 \end{aligned}$
::y 25x+7

$\begin{aligned} y = \frac{2}{4} x - 5 \end{aligned}$
::y=24x-5

$\begin{aligned} y = - 5 x - 2 \end{aligned}$
::y5x-2

$\begin{aligned} y = - x \end{aligned}$
::yx

$\begin{aligned} y = 4 \end{aligned}$
::y=4 y=4

$\begin{aligned} x = - 3 \end{aligned}$
::x% 3

$\begin{aligned} y = \frac{3}{2} x + 3 \end{aligned}$
::y=32x+3 y=32x+3

$\begin{aligned} y = - \frac{1}{6} x - 8 \end{aligned}$
::y16x-8

Graph $\begin{aligned} y = 4 \end{aligned}$ and $\begin{aligned} x = - 6 \end{aligned}$ on the same set of axes. Where do they intersect?
::在同一组轴上的 y= 4 和 x 6 图形。它们在哪里交叉 ?

If you were to make a general rule for the lines $\begin{aligned} y = b \end{aligned}$ and $\begin{aligned} x = a \end{aligned}$ , where will they always intersect?
::如果您为 y=b 和 x=a 线定出一条通则, 它们总是在哪里交叉 ?

The cost per month, $\begin{aligned} C \end{aligned}$ (in dollars), of placing an ad on a website is $\begin{aligned} C = 0.25 x + 50, \end{aligned}$ where $\begin{aligned} x \end{aligned}$ is the number of times someone clicks on your link. How much would it cost you if 500 people clicked on your link?
::在网站上张贴广告的每月成本是C=0.25x+50, 其中x是点击链接的次数。500人点击您的链接需要多少钱?

Review (Answers)
::回顾(答复)

Click to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键。

章节大纲

常规

斜坡- 截取窗体中的图形线

Graphing a Line in Slope Intercept Form ::以斜坡截取窗体绘制线形图

Examples ::实例

Example 1 ::例1

Example 2 ::例2

Review ::回顾

Review (Answers) ::回顾(答复)

Graphing a Line in Slope Intercept Form
::以斜坡截取窗体绘制线形图

Examples
::实例

Example 1
::例1

Example 2
::例2

Review
::回顾

Review (Answers)
::回顾(答复)