Course: 2.7 标准表格中的线形图

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Scott and Brooke are organizing a fundraiser for their school. They are planning a pasta dinner, where adult tickets will cost $16 and kids' tickets will cost $8. Their goal is to make $2000. If they sell only adult tickets, how many must they sell to reach their goal? If they sell only kids' tickets, how many must they sell to reach their goal?
::斯科特和布鲁克正在为他们的学校组织一场募捐活动。他们正在计划一场面食晚宴,成人票价为16美元,儿童票价为8美元。他们的目标是赚2 000美元。如果他们只卖成人票,他们要卖多少票才能达到目标?如果他们只卖儿童票,他们要卖多少票才能达到目标?

Graphing a Line in Standard Form
::在标准表格中绘制一条线

When a line is in standard form , there are two different ways to graph it. The first approach is to change the equation to slope-intercept form and then graph it. The second approach is to use standard form to find the $\begin{aligned} x \end{aligned}$ and $\begin{aligned} y - \end{aligned}$ intercepts of the line and connect the two.
::当一条线以标准形式出现时,有两种不同的图表方式。第一种方法是将方程式改为斜度截面,然后将其图形化。第二种方法是使用标准格式查找线的 x 和 y- 截面,并将两者连接起来。

Let's g raph $\begin{aligned} 5 x - 2 y = - 15 \end{aligned}$ .
::让我们用图5x2y+15。

Let’s use approach #1; change the equation to slope-intercept form.
::让我们使用第1进点; 将方程改为斜坡界面。

$\begin{aligned} 5 x - 2 y & = - 15 \\ - 2 y & = - 5 x - 15 \\ y & = \frac{5}{2} x + \frac{15}{2} \end{aligned}$

::5x-2y15-2y5x-15y=52x+152

The $\begin{aligned} y - \end{aligned}$ intercept is $\begin{aligned} (0, \frac{15}{2}) \end{aligned}$ . Change the improper fraction to a decimal and approximate it on the graph, (0, 7.5). Then use triangles. If you find yourself running out of room “rising 5” and “running 2,” you could also “fall 5” and “ run backwards 2” to find a point on the other side of the $\begin{aligned} y - \end{aligned}$ intercept.
::y- 界面是 (0, 152) 。将错误的分数修改为小数小数, 并在图表上接近它, (0, 7. 5) 。然后使用三角形。如果您发现自己正在从房间“ 上升 5 ” 和 “ 运行 2” 中跑出来, 您也可以“ 跌落 5 ” 和“ 向后跑 2 ” 在 y- 界面的另一侧找到一个点。

Now, let's find the x and y intercepts of the equation $\begin{aligned} 4 x - 3 x = 21 \end{aligned}$ and then graph this equation.
::现在,让我们找到方程 4x-3x=21的 x 和 Y 拦截,然后绘制这个方程图。

The other coordinate will be zero at these points. Therefore , for the $\begin{aligned} x - \end{aligned}$ intercept, plug in zero for $\begin{aligned} y \end{aligned}$ and for the $\begin{aligned} y - \end{aligned}$ intercept, plug in zero for $\begin{aligned} x \end{aligned}$ .
::其他坐标在这些点为零。因此, 对于 X- intercut, 插入为零 y 和 y- intercet, 插入为零 x 。

$\begin{aligned} 4 x - 3 (0) & = 21 & 4 (0) - 3 y = 21 \\ 4 x & = 21 & - 3 y = 21 \\ x & = \frac{21}{4} o r 5.25 & y = - 7 \end{aligned}$

::4x-3(0)=214(0)-3y=214x=21-3y=21x=214或5.25y=7

Let's use approach #2 from above. Plot each intercept on their respective axes and draw a line to connect them.
::让我们从上面走近2号路。将每个拦截点划在各自的轴上, 并绘制一条连接它们的线。

Examples
::实例

Example 1
::例1

Earlier, you were asked to find the number of adult and kids' tickets Scott and Brooke must sell to reach their goal.
::早些时候,你被要求寻找成人和孩子的票数斯科特和布鲁克必须卖达到他们的目标。

The equation, in standard form, for the pasta dinner sales goal is $\begin{aligned} 2000 = 16 x + 8 y \end{aligned}$ . If they sell only adult tickets, we are looking for the x -intercept, so set y equal to zero.
::标准格式的方程式, 面食销售目标为 2000= 16x+8y。如果它们只卖成人票, 我们要找的就是 X 拦截, 所以设定为 y 等于零。

$\begin{aligned} 2000 = 16 x + 8 (0) \\ 2000 = 16 x \\ x = 125 \end{aligned}$

::2000=16x+8(0)2000=16xx=125

Therefore, they must sell 125 adult tickets to reach their goal.
::因此,他们必须出售125张成人机票,才能达到他们的目标。

If they sell only kids' tickets, we are looking for the y -intercept, so set x equal to zero.
::如果他们只卖孩子的票, 我们在找 Y 拦截, 所以设置x等于零。

$\begin{aligned} 2000 = 16 (0) + 8 y \\ 2000 = 8 y \\ y = 250 \end{aligned}$

::2000=16(0)+8y2000=8yyy=250

Therefore, they must sell 250 kids' tickets to reach their goal.
::因此,他们必须卖掉250张孩子的机票,才能达到他们的目标。

Example 2
::例2

Graph $\begin{aligned} 4 x + 6 y = 18 \end{aligned}$ by changing it into slope-intercept form.
::图4x+6y=18,通过将其改变为斜坡界面形式。

Change $\begin{aligned} 4 x + 6 y = 18 \end{aligned}$ into slope-intercept form by solving for $\begin{aligned} y \end{aligned}$ , then graph.
::通过 y 解答, 将 4x+6y=18 修改为斜坡界面, 然后图形。

$\begin{aligned} 4 x + 6 y & = 18 \\ 6 y & = - 4 x + 18 \\ y & = - \frac{2}{3} x + 3 \end{aligned}$

::4x+6y=186y4x+18y23x+3

Example 3
::例3

Graph $\begin{aligned} 5 x - 3 y = 30 \end{aligned}$ by plotting the intercepts.
::图5x-3y=30 绘制拦截图。

Substitute in zero for $\begin{aligned} x \end{aligned}$ , followed by $\begin{aligned} y \end{aligned}$ and solve each equation.
::x以零取代x,然后是y,解决每个方程式。

$\begin{aligned} 5 (0) - 3 y & = 30 & 5 x - 3 (0) = 30 \\ - 3 y & = 30 & 5 x = 30 \\ y & = - 10 & x = 6 \end{aligned}$

::5(0)-3y=305x-3(0)=30-3y=305x=305x=30y=10x=6

Now, plot each on their respective axes and draw a line.
::现在,在各自的轴上绘制一个线条。

Review
::回顾

Graph the following lines by changing the equation to slope-intercept form.
::通过将方程式修改为斜坡界面形式,绘制下行图。

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

$\begin{aligned} 3 x + 8 y = 16 \end{aligned}$
::3x+8y=16

$\begin{aligned} 4 x - 2 y = 10 \end{aligned}$
::4x-2yy=10

$\begin{aligned} 6 x + 5 y = - 20 \end{aligned}$
::6x+5y20

$\begin{aligned} 9 x - 6 y = 24 \end{aligned}$
::9-6y=24

$\begin{aligned} x + 4 y = - 12 \end{aligned}$
::x+4y+12

Graph the following lines by finding the intercepts.
::通过找到拦截物来绘制下行图。

$\begin{aligned} 2 x + 3 y = 12 \end{aligned}$
::2x+3y=12

$\begin{aligned} - 4 x + 5 y = 30 \end{aligned}$
::- 4x+5y=30

$\begin{aligned} x - 2 y = 8 \end{aligned}$
::x-2yy=8

$\begin{aligned} 7 x + y = - 7 \end{aligned}$
::7+y7

$\begin{aligned} 6 x + 10 y = 15 \end{aligned}$
::6x+10y=15

$\begin{aligned} 4 x - 8 y = - 28 \end{aligned}$
::4-8y28

$\begin{aligned} y = 3 \end{aligned}$
::y=3 y=3

Writing Which method do you think is easier? Why?
::你觉得哪一种写法比较容易?

Writing Which method would you use to graph $\begin{aligned} x = - 5 \end{aligned}$ ? Why?
::您在图形 x% 5 中使用哪种方法 ? 为什么 ?

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。

Section outline

General

a 标准表格中的图表线

Graphing a Line in Standard Form ::在标准表格中绘制一条线

Examples ::实例

Example 1 ::例1

Example 2 ::例2

Example 3 ::例3

Review ::回顾

Review (Answers) ::回顾(答复)

Graphing a Line in Standard Form
::在标准表格中绘制一条线

Examples
::实例

Example 1
::例1

Example 2
::例2

Example 3
::例3

Review
::回顾

Review (Answers)
::回顾(答复)