Final answer:
The slope of a line that is perpendicular to the line with the equation y = -1/2x + 5 is 2. This is because perpendicular lines have slopes that are negative reciprocals of each other.
Step-by-step explanation:
The question asks about the slope of a line that is perpendicular to another line with a given equation. The equation of the given line is y = -1/2x + 5. Perpendicular lines have slopes that are negative reciprocals of each other. Since the slope of the given line is -1/2, the slope of a line perpendicular to it would be the negative reciprocal of -1/2, which is 2.
To understand the concept of perpendicular slopes, consider that the product of their slopes is -1. For the given line, the slope, represented as 'm' in the slope-intercept form y = mx + b, is negative, indicating that the line moves downward across the graph as x increases. In contrast, a line perpendicular to it will have a positive slope, moving upward as x increases.
Remember that a positive slope means that the line rises as it moves from left to right, while a negative slope means the line falls. The more positive the slope, the steeper the line rises, and conversely, the more negative the slope, the steeper the line falls.