Final answer:
The equation of the line that is perpendicular to the line with equation y = 2x + 5 and passes through the point (-2, 5) is y = (-1/2)x + 6.
Step-by-step explanation:
The question is asking for the equation of a line that is perpendicular to another line and passes through a specific point. To find this equation, we first need to determine the slope of the original line, which is given by y = 2x + 5. The slope here is 2. A line perpendicular to this would have a slope that is the negative reciprocal of 2, which means the slope of the perpendicular line is -1/2. Next, we use the point-slope form of a line to express the equation of the line that passes through the point (-2,5). The point-slope form is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point.
Substituting the known values, we get y - 5 = (-1/2)(x + 2). Finally, we simplify this equation to get it into the slope-intercept form y = mx + b, resulting in the equation of the perpendicular line: y = (-1/2)x + 6.