Final answer:
To find the equation of a line perpendicular to a given line, find the negative reciprocal of the slope of the given line and use the point-slope form of a linear equation.
Step-by-step explanation:
To find the equation of a line perpendicular to a given line, we need to find the negative reciprocal of the slope of the given line. The given line has the equation y = x + 5 - 3, which can be rewritten as y = x + 2. The slope of this line is 1. The negative reciprocal of 1 is -1/1, which simplifies to -1.
Now we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. We are given the point P(3, -3) and the slope -1. Plugging in these values, we get y - (-3) = -1(x - 3), which simplifies to y + 3 = -x + 3. Rearranging the equation, we have y = -x. Therefore, the equation of the line perpendicular to y = x + 2 that contains point P(3, -3) is y = -x.