Final answer:
The equation that describes a line perpendicular to 7x - y = 25 and passes through (2, 5) is found using the negative reciprocal of the original line's slope, which leads to the equation y - 5 = -1/7(x - 2).
Step-by-step explanation:
The question asked which equation describes a line that is perpendicular to the line given by the equation 7x - y = 25 and passes through the point (2, 5). To find the answer, we note that a line perpendicular to another line will have a slope that is the negative reciprocal of the original line's slope. The slope of the given line is 7 (since it can be rewritten in slope-intercept form as y = 7x - 25), therefore the slope of the perpendicular line is -1/7.
Using the point-slope form, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point on the line, we plug in our values: y - 5 = -1/7(x - 2). This simplifies to choice (c), which is correct and can also be written as y - 5 = -1/7x + 2/7.