Final answer:
The slope of the line passing through the origin and the point (3,5) is calculated using the coordinates (0,0) for the origin and (3,5) for the point. The slope is 5 divided by 3, which is 5/3.
Step-by-step explanation:
To find the slope of the line that passes through the origin and the point (3,5), we can use the slope formula, which is the change in y divided by the change in x (rise over run). Since the line passes through the origin (0,0) and (3,5), we subtract the coordinates of the origin from those of the point (3,5) to find the slope:
Slope (m) = (y2 - y1) / (x2 - x1) = (5 - 0) / (3 - 0) = 5/3
Therefore, the correct answer is A: 5/3. This represents that for every 3 units increase in x, there is a 5 units increase in y. It is important to note that the slope remains the same all along a straight line, regardless of the points used to calculate it, as long as they lie on the same line.