【官方】SAT数学每日一题附答案和解析(2018年1月12日)

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MathematicsStandard Multiple Choice

Read the following SAT test question and thenclick on a button to select your

answer.

y=x+a

y=-x+a

In the system of equations above, a is a positive constant. If the system is

graphed in the xy-plane, which of the following best describes the two

lines?

A.Both equations represent the same line.

B.The lines are parallel.

C.The lines are perpendicular.

D.The lines intersect but are not perpendicular.

答案：C

解析：

Let's examine the slope and y-intercept of both graphs.

Both equations are written in slope-intercept form: y=mx+b

where m is the graph's slope and b is the graph's y-intercept.

The graph of the first equation, y=x+a, has a slope of 1 and its y-intercept

is a.

The graph of the second equation, y=-x+a, has a slope of -1. Its y-intercept

is also a. Therefore, the y-intercepts are the same; the slope of the first

equation's graph is the negative of the reciprocal of the slope of the second

equation's graph (the reciprocal of 1/1 is 1/1), which means that the lines are

perpendicular.