Final answer:
The equation of the line that passes through the point (2, -3) and is parallel to the line 5x - 2y = 2 is y = 5/2x - 7/2.
Step-by-step explanation:
To find the equation of a line parallel to the given line, we need to find the slope of the given line first.
The given line is 5x - 2y = 2, which can be rewritten as -2y = -5x + 2 or y = 5/2x - 1.
Since the line we are looking for is parallel to this line, it will also have a slope of 5/2.
Using the point-slope form of a linear equation with the point (2, -3), we can write the equation of the line as y - (-3) = 5/2(x - 2).
Simplifying the equation gives us y = 5/2x - 7/2.
Therefore, the equation of the line that passes through the point (2, -3) and is parallel to the line 5x - 2y = 2 is y = 5/2x - 7/2.