Final answer:
To find the equation of a line perpendicular to another line, determine the slope of the given line and then use the point-slope form of the equation of a line with the given point.
Step-by-step explanation:
To find the equation of a line perpendicular to another line, we first need to determine the slope of the given line. The given line can be rewritten in the slope-intercept form as y = -2x - 6. The slope of this line is -2. Since a line perpendicular to another line has a negative reciprocal slope, the slope of the line we are looking for is 1/2.
Given that the line passes through the point P(2, 3), we can use the point-slope form of the equation of a line: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Substituting the values, we get y - 3 = 1/2(x - 2). Simplifying, we have y - 3 = 1/2x - 1. Rearranging the equation, we get y = 1/2x + 2.