Question

What is the equation in point-slope form of the line that crosses the x-axis at -1 and is perpendicular to the line represented by y = (1/2)x + 6?

A) y = -2x - 2
B) y = -2x - 1
C) y = 2x + 1
D) y = 2x - 1

Answer 1

To find the equation of the line perpendicular to y = (1/2)x + 6 that crosses the x-axis at -1, we determine that the slope is -2 and use the point-slope form with the point (-1, 0), resulting in the equation y = -2x - 2.

Step-by-step explanation:

The question asks for the equation of a line in point-slope form that crosses the x-axis at -1 and is perpendicular to the line y = (1/2)x + 6. The slope of this given line is 1/2, and the slope of a line perpendicular to it will be the negative reciprocal. Therefore, the perpendicular line will have a slope of -2.

Since the line crosses the x-axis at -1, the point of intersection is (-1, 0). Using the point-slope form y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point on the line, we plug in the slope -2 and the point (-1, 0):

y - 0 = -2(x - (-1))

y = -2x - 2

Therefore, the correct answer is A) y = -2x - 2.