# SAT考试数学考点之线性方程精讲

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SAT数学部分所考查的知识点，包括基础代数、数据分析&实际问题、中级代数三个部分，对于中国学生而言，这些知识点难度不大，但部分知识点考查的方式与侧重点和国内考试有些差异，需要注意。

### 1.2线性方程

#### 线性函数的表现形式：

The general form of theequation is

The slope-intercept form is

The slope of the line is representedby m and is defined to be the ratio of, where and are any two points on theline. The y-intercept is b.

The slope-point form is

#### 直线的位置关系：

If the slopes if line l and kare each defined (that is, if neither line is a vertical line), then

1line l and k are parallel if and only if theyhave the same slope;

2Line l and line k are perpendicular if and onlyif the product of their slopes is -1.

(A)(0, -1)

(B)(1, 1)

(C)(2, 3)

(D)(3, 2)

Solution

g(x)的斜率为，过(0,4)点，所以直线方程为：

(A) 1195 + 0.1x

(B) (1195 + 0.1)x

(C) 1195 + 10x

(D) (1195 + 1)x

Solution

1195为基础费用，10cents是每kWh的增加费用，所以总费用的方程为：

(A) x + 3y = 1

(B) 3x = –y + 5

(C) y – 3x = 4

(D) 6y = 2x – 1

Solution:

2y + 6x = 5是直线方程的一般形式，改写为斜截式：

，斜率为-3。再从选项中寻找斜率同样为-3的直线。

(A) The slope is four times steeper than f(x).

(B) The slope is four times less steep than f(x).

(C) All values of x are four times greater thanf(x) for the same values of y.

(D) The slope changes, but the y-interceptremains the same as f(x).

Solution

4f(x)的图像是将y轴拉伸4倍，4f(x)=8x+8。图像与X轴的交点不变，与Y轴的交点扩大4倍，斜率也增加4倍。

(A)f(x) = x + 3

(B)f(x) = x + 3

(C)f(x) = x

(D)f(x) = 2x

Solution:

### 练习：

|x – 3| ≤ 5

1. Which of the following inequalities isequivalent to the absolute value inequality above?

(A) –2 ≤ x ≤ 8

(B) –8 ≤ x ≤ 2

(C) x ≤ –2 or x ≥ 8

(D) x ≤ –8 or x ≥ 2

9992. Whichof the following equations could represent the linear equation above?

(A) y =–2x – 1

(B)  y =–2x + 1

(C)  y =2x – 1

(D) y = 2x+ 1

3. If f(x)is a linear function that passes through the points (4, 3) and (-4, -9), whatis the y-intercept of f(x)?

(A) (0, 2)

(B)  (2,0)

(C)  (0,-3)

(D) (-3,0)

4. Joel isa years older than Luca. In byears, Joel will be twice as old as Luca. What is Joel’s present age, in termsof a and b?

(A) –2(a – b)

(B) –2a – b

(C) 2a – b

(D) a – b

5. In the system of linear equations shown, ais a constant. If the system has no solution, what is the value of a?

A. 2

B. 3

C. 4

D. 5 6. What is the slope of the function in thegraph above?

7. If k is a rational number such that k >1, which of the following could be the graph of the equation y = key + ox + x +5? 1    2    3    4    5    6    7

A   C   C   C   C   C   A

1.    题干：|x – 3| ≤ 5等价于什么？

2.    题干：如何表示下图的直线？ 3.    题干：直线经过(4, 3) (-4, -9)，那么y轴截距是多少？

4.    题干：JLa岁，b年后，J的年龄会是L的两倍.现在J的年龄是多少？

5.    题干：如果

6.    题干：求斜率. 7.    题干：y = key + ox + x + 5的图像是哪一个？如果k是实数，而且k>1. （文章内容摘选自《新SAT非官方指南》

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