Final answer:
The equation of the line parallel to y = 2x + 3 and passes through (2, -1) is 2x - y = 5. So the correct answer is Option A.
Step-by-step explanation:
To find the equation of a line that is parallel to y = 2x + 3 and passes through the point (2, -1), we first recognize that parallel lines have the same slope. The slope of the given line is 2, so the slope of the parallel line will also be 2. Using the point-slope form of a linear equation, we can substitute the values of the point and the slope into the equation y - y1 = m(x - x1). Substituting the values, we get y - (-1) = 2(x - 2), which simplifies to y + 1 = 2x - 4. Rearranging the terms, the equation becomes 2x - y = 5. Therefore, the equation of the line that is parallel to y = 2x + 3 and passes through (2, -1) is 2x - y = 5 (Option A).