Question

What is the slope, m, of the line that is perpendicular to the line y = 1/6x + 9 and passes through the point (0, 7)?

a) -6
b) -1/6
c) 6
d) 1/6

Answer 1

The slope of a line perpendicular to another line with a slope of 1/6 is the negative reciprocal of 1/6, which is -6.

Step-by-step explanation:

The question is asking for the slope of a line that is perpendicular to another line with a slope of 1/6. In the context of algebra and coordinate geometry, the slope (m) of a line describes how steep the line is. For two lines to be perpendicular to each other in a Cartesian plane, the slopes of these lines have to be negative reciprocals of each other.

If the slope of the first line is 1/6, then the slope of a line perpendicular to it would be the negative reciprocal of 1/6, which is -6. Therefore, the correct answer is -6. This is because a slope of 1/6 means that for every 6 units of horizontal change, there is 1 unit of vertical change, and the perpendicular slope would need to reflect that relationship inversely.

It does not matter that the line passes through the point (0, 7), as this only affects the y-intercept of the line, not its slope. The slope is solely determined by the requirement for perpendicularity to the original line.