Final answer:
To find the equation of a line perpendicular to y = 2x - 5, we determine the negative reciprocal of the slope and use a given point to write the equation in point-slope form. and we get y = -1/2x - 4
Step-by-step explanation:
To find the equation of a line perpendicular to y = 2x - 5 and passing through the point (2, -5), we need to determine the slope of the given line and then find the negative reciprocal of that slope.
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 the equation, we can write the equation as y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope:
y - (-5) = -1/2(x - 2)
y + 5 = -1/2x + 1
y = -1/2x - 4