Final answer:
A line perpendicular to the line represented by 6x + y = 1 would have a slope that is the negative reciprocal of -6, hence a slope of 1/6. The general form of the equation is y = 1/6x + b, where 'b' is the y-intercept, which cannot be determined without further information.
Step-by-step explanation:
The question asks for an equation of a line that is perpendicular to the line represented by 6x + y = 1. In algebra, the slope of a line is of paramount importance when determining the relationship between two lines. For two lines to be perpendicular, their slopes must be negative reciprocals of each other.
First, we need to find the slope of the given line. We can rewrite the equation in slope-intercept form, y = mx + b, where m represents the slope. From 6x + y = 1, we can isolate y to get y = -6x + 1, indicating that the slope of this line is -6. Therefore, the slope of the perpendicular line must be ⅛, which is the negative reciprocal of -6.
The equation of the line perpendicular to 6x + y = 1 can be written in the form y = ⅛x + b. The value of b, the y-intercept, will depend on specific points through which the perpendicular line passes. Without additional information, we can only determine the slope of the perpendicular line.