Final answer:
The equation of the line parallel to y = 5/4x + 3/2 that passes through (-2,3) is y = 5/4x + 13/2. This is because parallel lines have identical slopes, and the equation must pass through the given point.
Step-by-step explanation:
The equation of the line parallel to y = 5/4x + 3/2 that passes through the point (-2,3) can be found using the concept that parallel lines have the same slope. The given line has a slope of 5/4, so the parallel line must also have a slope of 5/4. To find the equation of the line that passes through (-2,3) with the same slope, we use the point-slope form of a line: y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point.
Let's plug in our values: y - 3 = 5/4(x - (-2)) or y - 3 = 5/4(x + 2). Simplifying this equation, we distribute the slope across the (x + 2) term to get y - 3 = 5/4x + 5/2. Adding 3 to both sides to solve for y, we get y = 5/4x + 13/2, which is option C in the provided choices.