Final answer:
The correct equation in point-slope form for a line that is parallel to y=3x-2 and passes through the point P(4,7) is y - 7 = 3(x - 4).
Step-by-step explanation:
The subject of this question is to find the equation of a line in point-slope form, given that the line is parallel to another line and a point on the line is provided. To do this, we need to understand that two lines that are parallel have the same slope, and the slope is represented by the 'm' term in the line equation. Since the given line has an equation of y = 3x - 2, the slope (m) is 3. Now, using the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope, we can substitute the given point P(4,7) and the known slope to find the line's equation.
The point-slope equation for line I, which passes through point P(4,7) and has a slope of 3, is y - 7 = 3(x - 4). This matches option c from the provided choices, indicating that this is the correct equation for line I.