Final answer:
The equation of the line perpendicular to y=2x-7 and passing through the point (3, 4) is y = -1/2x + 7.5.
Step-by-step explanation:
To find the equation of a line perpendicular to another line, we need to determine the negative reciprocal of the slope of the given line. The given line has a slope of 2, so the perpendicular line will have a slope of -1/2.
Using the point-slope form of a line, the equation of the perpendicular line can be written as y - y1 = m(x - x1), where (x1, y1) is the given point (3, 4) and m is the slope (-1/2).
Substituting these values into the equation, we have y - 4 = -1/2(x - 3). Simplifying further, we get y = -1/2x + 7.5, which is the equation of the line perpendicular to y = 2x - 7 and passing through the point (3, 4).