Final answer:
To find the equation of a line parallel to y = -3x - 5 that passes through the point (2, -1), you can use the point-slope form of a line and substitute the given values to get the equation y = -3x + 5.
Step-by-step explanation:
To find the equation of a line parallel to y = -3x - 5 that passes through the point (2, -1), we need to find the slope of the given line and use it to construct the equation of the parallel line.
The given line is in the form y = mx + b, where m represents the slope and b represents the y-intercept.
From the given equation, we can see that the slope of the given line is -3.
Since the line parallel to the given line has the same slope, the slope of the parallel line is also -3.
Using the point-slope form of a line, we can write the equation of the parallel line as y - y1 = m(x - x1), where (x1, y1) is the point the line passes through.
Substituting the values (x1, y1) = (2, -1) and m = -3 into the equation, we can simplify to get y + 1 = -3(x - 2).
Further simplifying the equation gives us the final answer: y = -3x + 5.