Which choice could be the equation of a line perpendicular to the line represented by this equation?
y = 5
for this question, i put this:
y = -1/5x
but, it says i am wrong. how is that? 5 is 5/1, and so the negative reciprocal of 5/1 would be -1/5, right?
You are correct. Maybe they anticipated
(-1/5)*x, or -x/5, or -0.2x, or maybe they are just wrong.
y = 5 or y = 0x + 5
is a horizontal line with slope of 0
Thus a perpendicular line would be a vertical line, which has an undefined slope.
Any vertical line has the form x = k , where k is a constant
Yes, you are correct in thinking that the negative reciprocal of 5/1 is -1/5. However, in this case, the given equation y = 5 represents a horizontal line. Since the line is horizontal and parallel to the x-axis, any line perpendicular to it would be a vertical line parallel to the y-axis.
The equation of any vertical line can be written as x = constant, where the constant represents the x-coordinate of the points on the line. Therefore, the correct choice for the equation of a line perpendicular to y = 5 would be x = constant.
For example, x = 3, x = -2, x = 7, etc., would all be equations of lines perpendicular to y = 5.