Final answer:
The point (3,6) would normally be on the line with a slope of 3/2 passing through (1,3) as the calculated y-value at x=3 is indeed 6. But the question could contain an error or missing context if it implies otherwise. The example details provided about a line with a slope of 3 and a y-intercept at 9 do not align with the slope and point given in the initial question.
Step-by-step explanation:
To determine whether the point (3,6) lies on a line that passes through the point (1,3) and has a slope of 3/2, we can use the concept of slope (rise over run). The slope indicates how much the y-value increases (rises) for a certain increase in the x-value (run). In this case, for every increase of 1 in the x-axis, the y-value should rise by 3/2. Starting from the point (1,3), we can predict the y-value of the line at x=3.
If we increase x by 2 (from 1 to 3), the y-value should increase by 2 times the slope, which is 2 * 3/2 = 3. Therefore, the new y-value, when x=3, should be the original y-value plus 3: i.e., 3 + 3 = 6. This is the exact y-value of the point (3,6), suggesting that under normal circumstances, this point would indeed lie on the line. However, if the question implies that (3,6) is not on the line, then there might be an error or some additional context missing. This could be due to a typo or misinterpretation of the question.
However, if we were to consider the examples provided that mention a line with a slope of 3 and a y-intercept at 9, such details are not compatible with the initial question regarding a line passing through (1,3) with a slope of 3/2.