Final answer:
To find the slope, use the formula (change in y) / (change in x) with any two points from the table. The slope calculated using points (5, 8) and (10, 23) is 3.
Checking for proportional relationship shows that the ratio of y to x is not consistent, hence there is no proportional relationship.
Step-by-step explanation:
Finding the Slope and Proportional Relationship
To find the slope of a line using a set of points from a table, you will need to select any two points and use the formula:
slope = (change in y) / (change in x)
In this case, let's use the points (5, 8) and (10, 23) from the table provided. The change in y-value, or the rise, is 23 - 8 = 15, and the change in x-value, or the run, is 10 - 5 = 5. So the slope is:
slope = 15 / 5 = 3
However, to confirm a proportional relationship, every pair of x and y values in the table should have the same constant of proportionality (k), where k = y / x. Let's check this for each pair provided:
Since these k values are not equal, there is not a proportional relationship between the x and y values in the given table.
Lastly, for the data provided to form a dependence of y on x, we could graph the points and see if they lie in a straight line which ideally should pass through the origin if it's a truly proportional relationship, which in this table, it is not.