Final answer:
The slope of line p is 2; thus, line r will have a slope of -1/2 since it is perpendicular. Using the point (6, 4) that line r passes through, we find the equation of line r to be y = -1/2x + 7, which corresponds to option C.
Step-by-step explanation:
The question asks for the equation of line r, which is perpendicular to line p given by the equation 2x - y = -5. To find line r's equation, we first need to determine the slope of line p and then find the negative reciprocal of that slope because perpendicular lines have slopes that are negative reciprocals of each other. The slope of line p can be found from its equation in slope-intercept form, which is y = mx + b, where m is the slope. Converting 2x - y = -5 to the slope-intercept form gives us y = 2x + 5, which has a slope of 2. The negative reciprocal of 2 is -1/2. Since line r passes through the point (6, 4), we can use the point-slope form y - y1 = m(x - x1) to find its equation. Plugging in the values gives us y - 4 = -1/2(x - 6), which simplifies to y = -1/2x + 7. Therefore, the correct equation for line r is option C.