3.17 摘要:两种变量的线性等同和不平等

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• 选择节摘要:两个变量的线性等同和不平等

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  摘要:两个变量的线性等同和不平等

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  In this chapter, we learned about:
  ::在本章中,我们了解到:

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  Linear Models and Slope
  ::线性模型和斜体

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  • Determine if the ratio of the change in or distance between the y− values to the change in or distance between the x− values is constant. This ratio is the rate of change.
    ::确定 y - 值之间变化或距离与 x - 值之间变化或距离的比率是不变的。这个比率是变化率。
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  • Slope can be determined either by finding  $\begin{array}{r}m=\frac{rise}{run}\end{array}$  
    ::斜坡可以通过找到 m = 中空来决定
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  • Or, by using the formula $\begin{array}{r}m=\frac{y_2-y_1}{x_2-x_1}\end{array}$  
    ::或者,使用公式m=y2-y1x2-x1

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  Equations of Lines and Special Relationships Between Lines
  ::线的平线和线之间的特殊关系

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  • To write the equation of a line in slope-intercept form, $\begin{array}{r}y=mx+b\end{array}$ , identify the slope, m , and the y −intercept, (0, b ), and substitute for $\begin{array}{r}m\end{array}$  and  $\begin{array}{r}b\end{array}$ .    
    ::以斜坡截面格式写出线的方程式,y=mx+b,标明斜坡、m和y-截面(0,b),并替换m和b。
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  • Point-slope form ( $\begin{array}{r}y-y_1=m(x-x_1)\end{array}$ ): Identify the slope and a point on the line and then substitute for $\begin{array}{r}m\end{array}$  and $\begin{array}{r}(x_1,y_1)\end{array}$ .
    ::点窗体(y-y1=m(x-x1):标明斜坡和线上的一个点,然后取代m和(x1)y1。
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  • General form ( $\begin{array}{r}Ax+By=C\end{array}$ ): Write the equation in slope-intercept or point-slope form and then use inverse operations to get x and y on the same side of the equation and the number on the other side   
    ::一般窗体 (Ax+By=C): 以斜度截面或点窗体形式写入方程,然后使用反向操作获得方形同侧的 x 和 y 和另一侧的数字
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  • Horizontal lines have zero slope and their equations are of the form $\begin{array}{r}y=c\end{array}$ .
    ::水平线为零斜度,其方程式为y=c。
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  • Vertical lines have undefined slope and their equations are of the form $\begin{array}{r}x=c\end{array}$ .  
    ::垂直线有未定义的斜坡,其方程式为表x=c。
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  • Parallel lines are lines that never intersect. We can identify parallel lines by determining if their slopes are equal.
    ::平行线是永不交叉的线条。我们可以通过确定它们的斜坡是否相等来确定平行线条。
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  • Perpendicular lines meet at right angles and have slopes that are negative reciprocals of each other. 
    ::垂直线在右角相交,斜坡是相互负对等的斜坡。

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  Graphing Lines, Linear Inequalities and Absolute Value Functions
  ::图形线、线性不平等和绝对值函数

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  • To plot a point, first find the x− coordinate on the x− axis and find out where that meets the y− coordinate on the y −axis.
    ::绘制一个点, 首先在 x - 轴上找到x - 坐标, 并找出与 y - 轴上 y - 坐标相匹配的位置 。
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  • To graph a line by making a table of values, choose three x −values, find the y −values, plot the three points, and then draw a line through those points. 
    ::通过绘制数值表绘制线条图,选择三个 x - 值,找到 y - 值,绘制三个点,然后通过这些点绘制一条线。
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  • To graph a line by finding the intercepts, find the two intercepts, plot the intercepts, and draw a line through those points. To find the x −intercept, set $\begin{array}{r}y=0\end{array}$ . To find the y− intercept, set $\begin{array}{r}x=0\end{array}$ .
    ::要通过查找拦截物绘制线条图, 找到两个拦截物, 绘制拦截物图, 并通过这些点绘制一条线条。 要找到 x - 拦截物, 设置 y=0 。 要找到 y - 拦截物, 设置 x=0 。
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  • To graph a line using the point-slope method: Find a starting point to work from. Plot the starting point. Then, identify the rise and the run of the slope. The rise will tell you how many boxes to go up or down. (Take care of the sign of the slope with the rise). Go to the right the number of boxes in the run. From the starting point, follow the rise and run to find another point on the graph. Repeat this process again from the new point to get at least three points and connect them to form the line.
    ::使用点倾斜法绘制线条图 : 寻找要工作的起始点 。 绘制起始点 。 然后, 标明斜坡的上升和运行点 。 向上和向下将显示多少个框 。 (注意斜坡的标志和向上) 。 向右移动的框数 。 从起始点, 跟随向上并运行在图形上找到另一个点 。 从新点再次重复此进程, 以获得至少三个点, 并将其连接到线条 。
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  • To graph linear inequalities, graph the boundary line. If the inequality is >  or <, then the line will be dashed. If the inequality is ≥ or ≤, then the line is solid. Next, determine which region is included in the solution by using a test point.
    ::要绘制线性不平等图,请绘制边界线。如果不平等值为 > 或 < ,则线条会被冲破。如果不平等值为 _ 或 ,则线条是固态的。接下来,通过使用测试点确定解决方案中包含哪个区域 。
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  • To graph absolute value functions, find the vertex, choose three x- values on each side of the x- value for the vertex, use a table of values to find the y- values, plot the points and connect them in a V-shape. 
    ::要图形绝对值函数,请找到顶点,在顶点的 X 值的每侧选择三个 x 值,使用一个数值表查找 y 值,在 V 形状中绘制点并连接它们。

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  Looking Back, Looking Forward
  ::回顾,展望未来

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  In this chapter, we considered linear relationships, either equalities or inequalities. As we have seen, there are many relationships that can be modeled linearly: your cellphone bill, how surgeons' make cuts for surgery, and converting from Celsius to Fahrenheit temperature.
  ::在本章中,我们考虑了线性关系,要么是平等关系,要么是不平等关系。 正如我们所看到的,有很多关系可以线性模式建模:你的手机帐单,外科医生如何削减手术,以及从摄氏度到华氏温度的转换。

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  In the next chapter, we will compare linear relationships to each other. Considering a group of linear relationships at one time is called a system of equations or inequalities.
  ::在下一章中,我们将对线性关系进行比较。 一次考虑一组线性关系就被称为方程或不平等体系。

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  Chapter  Review
  ::回顾章次审查