Final answer:
The equation of a line that is perpendicular to the line y = -2x + 1 is one with a slope of 0.5. Upon reviewing the options, the correct answer is option d, which becomes y = -0.5x + 3 after rearrangement, aligning with the needed perpendicular slope of 1/2.
Step-by-step explanation:
To find the equation of a line that is perpendicular to another line, we need to use the concept of slope. For the given equation y = -2x + 1, the slope is -2. A line perpendicular to this one must have a slope that is the negative reciprocal of -2, which is ½. We can express this new slope as 1/2 or simply 0.5.
Keeping the slope-intercept form y = mx + b in mind, the slope (m) represents the steepness of the line, and the y-intercept (b) is where the line crosses the y-axis. Thus, any line with a slope of 1/2 would be perpendicular to the original line. Looking at the provided options, we need to find an equation with a slope of 0.5. When we rearrange option d. 2y = -x + 6 by dividing everything by 2, we get y = -0.5x + 3, reflecting the needed slope of 1/2 and thus being perpendicular to the original line.
Therefore, the correct answer in the slope-intercept form is d. y = -0.5x + 3 after rearranging it from its given form.