节: 水平和垂直线图 | 4.4 水平和垂直线图

章节大纲

Horizontal and Vertical Line Graphs
::水平和垂直线图

How do you graph equations of horizontal and vertical lines? See how in the example below.
::您如何绘制水平线和垂直线的方程式? 请参见下面的例子。

“Mad-cabs” have an unusual offer going on. They are charging $7.50 for a taxi ride of any length within the city limits. Graph the function that relates the cost of hiring the taxi "> $\begin{aligned} (y) \end{aligned}$ to the length of the journey in miles $\begin{aligned} (x) \end{aligned}$ .
::“Mad-cabs”的报价不同寻常,他们向市内任何长的出租车收费7.50美元,将租用出租车的费用与行程的里程(x)联系起来。

To proceed, the first thing we need is an equation . You can see from the problem that the cost of a journey doesn’t depend on the length of the journey. It should come as no surprise that the equation then, does not have $\begin{aligned} x \end{aligned}$ in it. Since any value of $\begin{aligned} x \end{aligned}$ results in the same value of $\begin{aligned} y (7.5) \end{aligned}$ , the value you choose for $\begin{aligned} x \end{aligned}$ doesn’t matter, so it isn’t included in the equation. Here is the equation:
::要继续,我们首先需要的是方程。你可以从一个问题中看到,旅程的成本并不取决于旅程的长度。那么,这个方程没有 x 并不令人惊讶。由于x 的任何值都得出与 y( 7. 5) 相同的值, 因此您选择的 x 值并不重要, 所以它没有包括在方程中。这里的方程是:

$\begin{aligned} y = 7.5 \end{aligned}$
::y=7.5 y=7.5

The graph of this function is shown below. You can see that it’s simply a horizontal line.
::此函数的图示显示在下面。您可以看到它只是一条水平线。

Any time you see an equation of the form “ $\begin{aligned} y = \end{aligned}$ constant ,” the graph is a horizontal line that intercepts the $\begin{aligned} y - \end{aligned}$ axis at the value of the constant.
::当您看到“y=常数”形式的方程式时, 图形是一条水平线, 以常数的值截取 y- 轴。

Similarly, when you see an equation of the form $\begin{aligned} x = \end{aligned}$ constant, then the graph is a vertical line that intercepts the $\begin{aligned} x - \end{aligned}$ axis at the value of the constant. (Notice that that kind of equation is a relation , and not a function, because each $\begin{aligned} x - \end{aligned}$ value (there’s only one in this case) corresponds to many (actually an infinite number) $\begin{aligned} y - \end{aligned}$ values.)
::同样,当您看到窗体 x= 常量的方程式时,图形是一条垂直线,以常量的值截取 x- 轴值。 (注意,这种方程式是一种关系,而不是函数,因为每个 x- 值(在此情况下只有一个)都对应许多 y- 值(实际上是一个无限的数字) y- 值。)

Plotting Graphs
::绘图图图

Plot the following graphs.
::绘制下图。

(a) $\begin{aligned} y = 4 \end{aligned}$
:a)y=4

$\begin{aligned} y = 4 \end{aligned}$ is a horizontal line that crosses the $\begin{aligned} y - \end{aligned}$ axis at 4.
::y=4 是一条水平线, 4 时横跨 y- 轴。

(b) $\begin{aligned} y = - 4 \end{aligned}$
:b) y4

$\begin{aligned} y = - 4 \end{aligned}$ is a horizontal line that crosses the $\begin{aligned} y - \end{aligned}$ axis at −4.
::y4 是一条横线, 横跨 y - 轴的 y 4 。

(c) $\begin{aligned} x = 4 \end{aligned}$
:c) x=4

$\begin{aligned} x = 4 \end{aligned}$ is a vertical line that crosses the $\begin{aligned} x - \end{aligned}$ axis at 4.
::x=4 是一条垂直线, 横跨 x - 轴 4 时的 x - 轴。

(d) $\begin{aligned} x = - 4 \end{aligned}$
:d) x4

$\begin{aligned} x = - 4 \end{aligned}$ is a vertical line that crosses the $\begin{aligned} x - \end{aligned}$ axis at −4.
::x4 是一条垂直线, 横跨 x - 轴 4 的 x - 轴。

Finding an Equation
::查找等量

Find an equation for the $\begin{aligned} x - \end{aligned}$ axis and the $\begin{aligned} y - \end{aligned}$ axis.
::查找 x - 轴和 y - 轴的方程式。

Look at the axes on any of the graphs from previous examples. We have already said that they intersect at the origin (the point where $\begin{aligned} x = 0 \end{aligned}$ and $\begin{aligned} y = 0 \end{aligned}$ ). The following definition could easily work for each axis.
::查看先前示例中任何图表的轴。我们已经说过, 这些轴在来源处交叉( x=0 和 y=0 的点 ) 。以下定义很容易为每个轴工作。

$\begin{aligned} x - \end{aligned}$ axis: A horizontal line crossing the $\begin{aligned} y - \end{aligned}$ axis at zero.
::x- 轴: 横线在零时横过 y- 轴。

$\begin{aligned} y - \end{aligned}$ axis: A vertical line crossing the $\begin{aligned} x - \end{aligned}$ axis at zero.
::y-轴:一条垂直线在零时穿过 x-轴线。

So using example 3 as our guide, we could define the $\begin{aligned} x - \end{aligned}$ axis as the line $\begin{aligned} y = 0 \end{aligned}$ and the $\begin{aligned} y - \end{aligned}$ axis as the line $\begin{aligned} x = 0 \end{aligned}$ .
::因此,以例3作为我们的指南, 我们可以将 x - 轴定义为 y=0 线, y - 轴定义为 x=0 线。

Example
::示例示例示例示例

Example 1
::例1

Write the equation of the horizontal line that is 3 units below the x-axis .
::写入 X 轴下方3 个单位的水平线的方程式。

The horizontal line that is 3 units below the x-axis will intercept the y-axis at $\begin{aligned} y = - 3 \end{aligned}$ . No matter what the value of x, the y value of the line will always be -3. This means that the equations for the line is $\begin{aligned} y = - 3 \end{aligned}$ .
::x 轴下方的 3 个单位的水平线将拦截 Y 轴 y 3 。无论 x 值是多少, 该线的 y 值总是 - 3 。这意味着该线的方程式是 y 3 。

Review
::回顾

Write the equations for the five lines ( $\begin{aligned} A \end{aligned}$ through $\begin{aligned} E \end{aligned}$ ) plotted in the graph below.

::在下图中绘制五个行(A至E)的方程。

For 2-10, use the graph above to determine at what points the following lines intersect.
::2-10时,使用上图确定在什么点上以下线交叉。

$\begin{aligned} A \end{aligned}$ and $\begin{aligned} E \end{aligned}$
::A和E

$\begin{aligned} A \end{aligned}$ and $\begin{aligned} D \end{aligned}$
::A和D

$\begin{aligned} C \end{aligned}$ and $\begin{aligned} D \end{aligned}$
::C和D

$\begin{aligned} B \end{aligned}$ and the $\begin{aligned} y - \end{aligned}$ axis
::B和y-轴

$\begin{aligned} E \end{aligned}$ and the $\begin{aligned} x - \end{aligned}$ axis
::E 和 x- 轴

$\begin{aligned} C \end{aligned}$ and the line $\begin{aligned} y = x \end{aligned}$
::C 和 y=x 线 y=x

$\begin{aligned} E \end{aligned}$ and the line $\begin{aligned} y = \frac{1}{2} x \end{aligned}$
::E 行 Y=12x

$\begin{aligned} A \end{aligned}$ and the line $\begin{aligned} y = x + 3 \end{aligned}$
::A 和 y=x+3 线条

$\begin{aligned} B \end{aligned}$ and the line $\begin{aligned} y = - 2 x \end{aligned}$
::B 和 y2x 线

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

Horizontal and Vertical Line Graphs ::水平和垂直线图

Plotting Graphs ::绘图图图

Finding an Equation ::查找等量

Example ::示例示例示例示例

Example 1 ::例1

Review ::回顾

Review (Answers) ::回顾(答复)

Horizontal and Vertical Line Graphs
::水平和垂直线图

Plotting Graphs
::绘图图图

Finding an Equation
::查找等量

Example
::示例示例示例示例

Example 1
::例1

Review
::回顾

Review (Answers)
::回顾(答复)