Final answer:
The equation of the line parallel to y = -3x + 4 and passing through the point (5, 2) is y = -3x + 17. This is determined by using the same slope as the original line and solving for the y-intercept using the coordinates of the given point.
Step-by-step explanation:
The question asks for the equation of a line that is parallel to the given line y = -3x + 4 and passes through the point (5, 2). To find this line, we must use the fact that parallel lines have the same slope. Since the given line has a slope of -3, our new line will also have a slope of -3.
The general form of the equation of a line is y = mx + b, where m is the slope and b is the y-intercept. In this scenario, we already know that m = -3 for our new line. Now, we need to find the y-intercept b by plugging in the coordinates of the given point (x=5, y=2) from which our line should pass through:
y = mx + b
2 = (-3)(5) + b
2 = -15 + b
b = 17
Thus, the equation of our parallel line is y = -3x + 17.