axis of ordinates

简明释义

纵坐标轴

英英释义

例句

1.In the Cartesian coordinate system, the vertical line is known as the axis of ordinates (纵坐标轴).

在笛卡尔坐标系统中，垂直线被称为axis of ordinates（纵坐标轴）。

2.In this graph, the axis of ordinates (纵坐标轴) represents the temperature in degrees Celsius.

在这个图表中，axis of ordinates（纵坐标轴）表示摄氏度的温度。

3.To analyze the trend, we need to examine the values on the axis of ordinates (纵坐标轴).

为了分析趋势，我们需要检查axis of ordinates（纵坐标轴）上的值。

4.The data points are plotted against the axis of ordinates (纵坐标轴) to show their relationship.

数据点是相对于axis of ordinates（纵坐标轴）绘制的，以显示它们之间的关系。

5.When plotting a graph, make sure to label the axis of ordinates (纵坐标轴) correctly.

绘制图表时，请确保正确标记axis of ordinates（纵坐标轴）。

作文

In the study of mathematics and geometry, particularly in the context of graphing equations, we often encounter various terms that describe the components of a coordinate system. One such term is the axis of ordinates, which plays a crucial role in understanding how to plot points on a two-dimensional plane. The axis of ordinates is commonly known as the y-axis, which runs vertically and is used to represent the values of the dependent variable in a function or equation. To better grasp the significance of the axis of ordinates, we can visualize a standard Cartesian coordinate system. This system consists of two perpendicular lines: the horizontal line, called the x-axis, and the vertical line, known as the axis of ordinates. These axes intersect at a point called the origin, which has coordinates (0,0). The x-axis typically represents the independent variable, while the axis of ordinates represents the dependent variable.When we graph a function, we plot points based on the relationship between these two variables. For example, consider the linear equation y = 2x + 1. To graph this equation, we need to choose values for x and calculate the corresponding values for y. If we select x = 0, we find that y = 1. This point, (0,1), lies on the axis of ordinates at the value of 1. Similarly, if we choose x = 1, we calculate y = 3, giving us another point (1,3) that we can plot on the graph. The axis of ordinates not only helps us plot points but also allows us to interpret the behavior of functions visually. By analyzing the slope and intercepts of a line, we can determine how changes in the independent variable affect the dependent variable. For instance, in our previous example, the slope of 2 indicates that for every unit increase in x, y increases by 2 units. This relationship is clearly illustrated when we look at the graph and see how the line rises steeply along the axis of ordinates.Moreover, the axis of ordinates is essential in more complex functions, such as quadratic or exponential functions. Each type of function exhibits unique characteristics when graphed, and the axis of ordinates helps us identify key features like vertex points, maximum or minimum values, and asymptotes. Understanding how to read and interpret these features on the axis of ordinates is vital for anyone studying advanced mathematics or engaging in fields that rely heavily on data analysis.In conclusion, the axis of ordinates is a fundamental aspect of the Cartesian coordinate system, serving as the vertical reference line for graphing functions. Its importance cannot be overstated, as it aids in visualizing relationships between variables, interpreting mathematical behavior, and analyzing complex functions. As students and professionals alike continue to explore the vast world of mathematics, a firm grasp of concepts like the axis of ordinates will undoubtedly enhance their understanding and application of mathematical principles in real-world scenarios.

在数学和几何的研究中，特别是在图形方程的背景下，我们经常会遇到描述坐标系组成部分的各种术语。其中一个术语是纵坐标轴，它在理解如何在二维平面上绘制点时起着至关重要的作用。纵坐标轴通常被称为y轴，它是垂直运行的，用于表示函数或方程中因变量的值。为了更好地理解纵坐标轴的重要性，我们可以想象一个标准的笛卡尔坐标系。这个系统由两条垂直线组成：水平线称为x轴，垂直线称为纵坐标轴。这些轴在一个称为原点的点相交，原点的坐标为(0,0)。x轴通常表示自变量，而纵坐标轴表示因变量。当我们绘制一个函数时，我们根据这两个变量之间的关系绘制点。例如，考虑线性方程y = 2x + 1。要绘制这个方程，我们需要选择x的值并计算相应的y值。如果我们选择x = 0，我们发现y = 1。这个点(0,1)位于纵坐标轴的1值处。类似地，如果我们选择x = 1，我们计算出y = 3，得到另一个点(1,3)，我们可以在图中绘制。纵坐标轴不仅帮助我们绘制点，还使我们能够直观地解释函数的行为。通过分析直线的斜率和截距，我们可以确定自变量的变化如何影响因变量。例如，在我们之前的例子中，斜率为2表示每增加一个单位的x，y增加2个单位。当我们查看图形并看到直线沿着纵坐标轴陡然上升时，这种关系得到了清晰的说明。此外，在更复杂的函数中，纵坐标轴也是必不可少的，例如二次函数或指数函数。每种类型的函数在绘图时都会表现出独特的特征，而纵坐标轴帮助我们识别关键特征，如顶点、最大或最小值和渐近线。理解如何在纵坐标轴上读取和解释这些特征对于任何学习高级数学或参与依赖大量数据分析的领域的人来说都是至关重要的。总之，纵坐标轴是笛卡尔坐标系的一个基本方面，作为绘制函数的垂直参考线，其重要性不容小觑，因为它有助于可视化变量之间的关系、解释数学行为以及分析复杂函数。随着学生和专业人士继续探索广阔的数学世界，对像纵坐标轴这样的概念的牢固掌握无疑将增强他们在实际场景中理解和应用数学原理的能力。