每日一题

Mathematics>Standard Multiple Choice

Read the following SAT test question and then click 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.

答案和解析

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.