which of the following is an equation of a line that is perpendicular to y=-2x+5 and passes through the point (-2,3)

To find a line that is perpendicular to a given line, we use the fact that the slopes of perpendicular lines are negative reciprocals.

The given line has a slope of -2. The negative reciprocal of -2 is 1/2.

Using the point-slope form of a line, (y - y₁) = m(x - x₁), where (x₁, y₁) = (-2, 3) and m = 1/2, we can substitute these values into the equation to find the line that passes through the point (-2, 3) and is perpendicular to y = -2x + 5.

y - 3 = 1/2(x - (-2))
y - 3 = 1/2(x + 2)

Expanding the equation:
y - 3 = 1/2x + 1
y = 1/2x + 4

Therefore, the equation of the line that is perpendicular to y = -2x + 5 and passes through the point (-2, 3) is y = 1/2x + 4.

Therefore, the correct answer is: y = 1/2x + 4.