Final answer:
The slope of a line perpendicular to the line with the equation y = (1/4)x + 7 is -4, since perpendicular slopes are negative reciprocals of each other. The correct answer is a) -4
Step-by-step explanation:
The slope of a line is a measure of how steep the line is and indicates how much 'y' changes for a change in 'x'. When you have the equation of a line in slope-intercept form, which is 'y = mx + b', the 'm' represents the slope. For the line represented by the equation y = (1/4)x + 7, the slope is 1/4.
Now, when two lines are perpendicular to each other, their slopes have a very specific relationship: their slopes are negative reciprocals of each other. This means that the product of their slopes is -1. To find the slope of a line that is perpendicular to the given line, you would therefore take the negative reciprocal of 1/4, which is -4. This means the slope of the line perpendicular to the given line is -4, which corresponds to option a.