Final answer:
The equation of a line parallel to y = -2x - 5 and passing through the point (3, -2) is y = -2x + 4, since parallel lines have the same slope.
Step-by-step explanation:
To find the equation of a line parallel to the given line y = -2x - 5 and passing through the point (3, -2), you need to use the fact that parallel lines have the same slope. The slope of the given line is -2, because it is the coefficient of x in the equation. Therefore, the parallel line must also have a slope of -2.
Now you use the point-slope form of a line equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point through which the line passes. Plugging in the slope -2 and the point (3, -2), you get:
y - (-2) = -2(x - 3)
Simplifying this, we get:
y + 2 = -2x + 6
Finally, subtracting 2 from both sides gives us the equation of the parallel line:
y = -2x + 4