Correct Answer: D
Explanation:
To identify the first step that must be taken when constructing a perpendicular line, there is some information about the given line that needs to be clearly established first.
First recall what it means to be perpendicular. For lines to be perpendicular, their slopes must be opposite reciprocals of each other and they must have one point of intersection.
From here, look at the possible answers to decide which one is best.
"Find the x-intercept of the given line." doesn't necessarily help when constructing a perpendicular line.
"Take the negative reciprocal of the given line's slope." Taking this would give the slope of a perpendicular line but in order to do so the slope must be known of the given line.
"Calculate the slope of the given line." in order to construct a perpendicular line, the slope must be calculated on the given line.
"Either calculate the slope of the given line or identify the intersection point of the two lines." In order to construct a perpendicular line, the intersection point must be found and the slope of the given line must be found before the slope of the perpendicular line is found. Therefore, this is the best answer.