高一数学必修一第五章知识总结

高一数学必修一第五章知识总结
1.本章主要内容是关于一次函数及其应用。

The main content of this chapter is about linear functions and their applications.
2.一次函数的定义是f(x)=ax+b。

The definition of a linear function is f(x)=ax+b.
3.一次函数的图像是一条直线。

The graph of a linear function is a straight line.
4.一次函数的斜率表示为a，截距表示为b。

The slope of a linear function is represented by a, and the intercept is represented by b.
5.一次函数的斜率可以表示为Δy/Δx。

The slope of a linear function can be represented as
Δy/Δx.
6.斜率为正的一次函数是递增的，斜率为负的一次函数是递减的。

A linear function with a positive slope is increasing, while a linear function with a negative slope is decreasing.
7.一次函数的零点就是方程f(x)=0的解。

The zero point of a linear function is the solution to
the equation f(x)=0.
8.一次函数的图像经过坐标原点时，截距为零。

The graph of a linear function passes through the origin when the intercept is zero.
9.一次函数的图像是一条直线，其斜率决定了直线的倾斜程度。

The graph of a linear function is a straight line, and
its slope determines the steepness of the line.
10.对于两点(x1, y1)和(x2, y2)，一次函数的斜率可以表示为
(y2-y1)/(x2-x1)。

For two points (x1, y1) and (x2, y2), the slope of a linear function can be represented as (y2-y1)/(x2-x1).
11.一次函数的斜率可以用点斜式来表示为y-y1=a(x-x1)。

The slope of a linear function can be represented in point-slope form as y-y1=a(x-x1).
12.一次函数的斜率也可以用截距式来表示为y=ax+b。

The slope of a linear function can also be represented in slope-intercept form as y=ax+b.
13.一次函数的平行线具有相同的斜率。

Parallel lines of a linear function have the same slope.
14.一次函数的垂直线的斜率为无穷大。

The slope of a vertical line of a linear function is infinitely large.
15.一次函数的平行线之间的距离等于它们之间任一点的纵坐标的差的绝对值。

The distance between parallel lines of a linear function
is equal to the absolute difference of their y-coordinates at any point.
16.一次函数的垂直线之间的距离等于它们的横坐标的差的绝对值。

The distance between vertical lines of a linear function
is equal to the absolute difference of their x-coordinates.
17.一次函数的平行线的截距相等。

The intercept of parallel lines of a linear function is equal.
18.一次函数的垂直线的截距不存在。

The intercept of vertical lines of a linear function does not exist.
19.一次函数的解对应了线性方程的解。

The solution of a linear function corresponds to the solution of a linear equation.
20.一次函数的应用包括了直线运动、物品成本及收益的关系等。

The applications of linear functions include linear motion, cost and revenue relationships, etc.
21.点斜式是表示一次函数的直线方程的一种形式。

The point-slope form is a way to represent the linear equation of a linear function.
22.两点式是表示一次函数的直线方程的一种形式。

The two-point form is a way to represent the linear equation of a linear function.
23.斜率截距式是表示一次函数的直线方程的一种形式。

The slope-intercept form is a way to represent the linear equation of a linear function.
24.一次函数的值域是整个实数集。

The range of a linear function is the entire set of real numbers.
25.一次函数的定义域是整个实数集。

The domain of a linear function is the entire set of real numbers.
26.一次函数的图像是直线，它穿过网格线上的整点。

The graph of a linear function is a line that passes through the integer points on the grid.
27.一次函数的图像通常用直线图形来表示。

The graph of a linear function is usually represented by
a straight line.
28.一次函数的表达式中x的最高次是1。

The highest power of x in the expression of a linear function is 1.
29.一次函数的图像是右上方倾斜或右下方倾斜的直线。

The graph of a linear function is a line that slopes upward to the right or slopes downward to the right.
30.一次函数的导数是其斜率。

The derivative of a linear function is its slope.
31.一次函数的导数是常数。

The derivative of a linear function is a constant.
32.一次函数的导数与函数值的关系是对应的。

The relationship between the derivative and the function value is corresponding for a linear function.
33.一次函数的解析式是f(x)=ax+b。

The analytical expression of a linear function is
f(x)=ax+b.
34.一次函数的定理包括零点定理、中点定理和导数定理等。

The theorems of a linear function include the zero-point theorem, midpoint theorem, and derivative theorem, etc.
35.一次函数的图像可用斜率和截距来描述。

The graph of a linear function can be described by its slope and intercept.
36.一次函数的图像在坐标平面上是一条直线。

The graph of a linear function is a straight line on the coordinate plane.
37.一次函数的图像在坐标平面上是单值而不是多值。

The graph of a linear function on the coordinate plane is single-valued rather than multi-valued.
38.一次函数的图像可以通过已知的点和斜率来绘制。

The graph of a linear function can be plotted by known points and slope.
39.一次函数的图像的方向由斜率的正负决定。

The direction of the graph of a linear function is determined by the sign of the slope.
40.一次函数的斜率存在，且不等于零。

The slope of a linear function exists and is not equal to zero.
41.一次函数的截距可以为零、正值或者负值。

The intercept of a linear function can be zero, positive, or negative.
42.一次函数的截距表示了函数与y轴的交点。

The intercept of a linear function represents the intersection with the y-axis.
43.一次函数的零点是方程f(x)=0的解。

The zero point of a linear function is the solution of the equation f(x)=0.
44.一次函数的零点决定了直线与x轴的交点。

The zero point of a linear function determines the intersection of the line with the x-axis.
45.一次函数的定义域表示了函数的所有可能输入值。

The domain of a linear function represents all possible input values for the function.
46.一次函数的值域表示了函数的所有可能输出值。

The range of a linear function represents all possible output values for the function.
47.一次函数的定义域是(-∞, +∞)。

The domain of a linear function is (-∞, +∞).
48.一次函数的值域是(-∞, +∞)。

The range of a linear function is (-∞, +∞).
49.一次函数的导数是其斜率。

The derivative of a linear function is its slope.
50.一次函数的斜率等于其导数的值。

The slope of a linear function is equal to the value of its derivative.
51.一次函数的截距等于其导数在原点的函数值。

The intercept of a linear function is equal to the function value of its derivative at the origin.
52.一次函数的导函数是常数。

The derivative of a linear function is a constant.。