Final answer:
The equation of a line that is parallel to y = -3x - 5 and passes through (5,5) is y = -3x + 20.
Step-by-step explanation:
To find the equation of a line that is parallel to the line with the equation y = -3x - 5 and passes through the point (5,5), we need to use the fact that parallel lines have the same slope. The given line has a slope of -3, so our new line will also have a slope of -3.
Using the point-slope form of a line's equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line, we substitute the slope and the given point to find our equation.
Therefore, the equation of the line parallel to y = -3x - 5 and passing through (5,5) is y - 5 = -3(x - 5). Simplifying this equation by distributing the -3 and moving the 5 to the other side, we get y = -3x + 15 + 5, which simplifies to y = -3x + 20.