Question

A line passing through (,), and perpendicular to the line whose equation is

a) y = mx + b
b) y = -mx + b
c) y = mx - b
d) y = -mx - b

Answer 1

Option A. The student is asking for the equation of a line that is perpendicular to another line, with the original line's equations provided. The key to solving this problem is understanding that the perpendicular line will have a slope that is the negative reciprocal of the original line's slope.

Step-by-step explanation:

The student has asked about finding the equation of a line passing through a given point and perpendicular to another line. Any line perpendicular to a line with slope m will have a slope that is the negative reciprocal of m. In other words, if the slope of the original line is m, the perpendicular line’s slope will be -1/m. For the four equations given (a to d), they all represent different lines with different slopes and y-intercepts. The y-intercept, represented by b, indicates where the line crosses the y-axis.

For all these equations, the slope (m) and y-intercept (b) of the line are crucial in determining the equation of the line perpendicular to it. The slope dictates how steep the line is (rise over run), and the y-intercept is the point where the line crosses the y-axis. Therefore, for a line described by y = mx + b, a line perpendicular to this would have a slope of -1/m and would pass through the specified coordinate, which was not provided in the question.