Final answer:
The equation of line w, which is perpendicular to line v, is found by taking the negative reciprocal of the slope of line v (-7) to get the slope of line w (1/7) and using the point (10, 1) through which line w passes. After applying the point-slope form, the equation of line w is y = 1/7x - 3/7.
Step-by-step explanation:
To find the equation of line w, we must first understand the properties of perpendicular lines. Line v is given by the equation y - 10 = -7(x - 2). This can be rewritten in slope-intercept form as y = -7x + 24, which shows that line v has a slope of -7. For two lines to be perpendicular, their slopes must be negative reciprocals of each other. Therefore, if line v has a slope of -7, the slope of line w will be 1/7.
Since we know line w passes through the point (10, 1), we can use the point-slope form of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Substituting these values, we get y - 1 = 1/7(x - 10). Simplifying, we have y = 1/7x - 10/7 + 1 or y = 1/7x - 3/7 as the equation of line w.