Final answer:
To find the equation of a line perpendicular to another line, we find the negative reciprocal of the slope of the given line and use the point-slope form of the equation. In this case, the equation of the line is y = x + 3.
Step-by-step explanation:
To find the equation of a line that is perpendicular to another line, we need to determine the negative reciprocal of the slope of the given line. The given line has the equation y = 21 - x, which can be rewritten as y = -x + 21. The slope of this line is -1. The negative reciprocal of -1 is 1, so the slope of the perpendicular line is 1.
Since the perpendicular line passes through the point (0,3), we can use the point-slope form of the equation: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope. Substituting the values, we have y - 3 = 1(x - 0). Simplifying, we get y - 3 = x, or y = x + 3.
Therefore, the equation of the line that passes through the point (0,3) and is perpendicular to the line y = 21 - x is y = x + 3. So, the correct answer is C.