Final answer:
The equation of a line parallel to y = (2/3)x + 1 and passing through the point (3,1) is y = (2/3)x - 1, which is option C.
Step-by-step explanation:
To find the equation of a line passing through the point (3,1) and parallel to y = (2/3)x + 1, we need to realize that parallel lines have the same slope. The given line has a slope of 2/3. Since the line we want to find is parallel to this, its slope must also be 2/3.
To find the equation of our line, we use the point-slope form of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through. Plugging in our values we get y - 1 = (2/3)(x - 3).
Let's simplify the equation:
- y - 1 = (2/3)x - 2
- y = (2/3)x - 2 + 1
- y = (2/3)x - 1
The correct equation is therefore y = (2/3)x - 1, which is option C.