Final answer:
The equation of line q, which is perpendicular to line p with equation y = -1/2x + 8 and passes through the point (4,7), is y = 2x - 1.
Step-by-step explanation:
The equation for line p can be written as y = -½x + 8. To find the equation of line q, which is perpendicular to line p, we need to determine the perpendicular slope. The slope of line p is -1/2, so the slope of line q will be the negative reciprocal, which is 2. Since line q passes through the point (4,7), we can use the point-slope form to create the equation y - y1 = m(x - x1) where m is the slope and (x1, y1) is the given point. Substituting, we get y - 7 = 2(x - 4). Simplifying, the equation of line q is y = 2x - 1.