Final answer:
The equation of a line that is perpendicular to the line with the equation y = 1/2x + 1 and passes through the point P(0,2) is y = -2x + 2.
Step-by-step explanation:
The equation of a line that is perpendicular to another line can be found by taking the negative reciprocal of the slope of the original line. The given line is y = 1/2x + 1, which has a slope of 1/2. A line perpendicular to this line will have a slope of -2 (negative reciprocal of 1/2). Since our line must go through the point P(0,2), we use this point to find the y-intercept.
The equation of the line in slope-intercept form, y = mx + b, becomes y = -2x + b. Plugging in the coordinates of point P gives us 2 = -2(0) + b, which simplifies to b = 2. Therefore, the equation of the line we are looking for is y = -2x + 2.