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SAT数学:代数例题 7

2019-08-29 SAT-数学 阅读

SAT Question 9 Article
Rank: Medium
难度: 中等
Topic: Algebra, Equation of a line
话题:代数,直线公式

 
Below is a question from a recent SAT exam. It is a non-calculator question that would typically take a student 1-2 minutes to complete.
下面是最近SAT考试中的一个问题。此问题不可使用计算机,学生通常需要1-2分钟来完成。


Which of the following is an equation of line in the
xy-plane above?
下面哪个选项是在xy平面上的直线ℓ的方程?
 

 
To begin, we must recall that the equation on a straight line comes in the form
首先,我们必须先回想一下直线的方程的形式


Where m is the slope and c is the y-intercept.
其中m是斜率,c是y轴的截距。

We will start by finding the y-intercept. This is the point where the line crosses the y-axis.
首先求y轴的截距c,这是直线ℓ与y轴相交的点。
 

We can clearly see in this diagram that the line meet the y-axis at -4. So we can replace c in our equation.
从这个图中我们可以清楚地看到直线与y轴在-4处相交。方程中的c为-4。

 


Now we need to find the slope of the line. To find this we use the formula:
现在我们需要求直线的斜率,需要用到斜率公式:

 

 
So we need to find to point on our line, any two will do but, I will pick the two points where it meets an axis.
我们需要在直线上找到任意两点,为了方便,要选它与坐标轴相交的两点。

(0, -4) & (-4,0)

So our two x-coordinates are 0 and -4 whilst our two y-coordinates are -4 and 0.
We can put these into the formula:
所以两个x坐标的值是0和-4,两个y坐标的值是-4和0。
把这些代入公式:

 


Therefore,
因此

 


We put this now into our equation for our line.
把m值代入直线方程。

 


We then can move x to the LHS of the equation.
把x移到方程的左边。

 


And we can see that the answer is C.
最后,答案是c


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