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To determine if y varies directly with x, we need to check if the ratio of y to x remains constant for all values in the table.
Let's calculate the ratios for each pair of x and y:
For the first pair (x=5, y=25): y/x = 25/5 = 5
For the second pair (x=10, y=50): y/x = 50/10 = 5
For the third pair (x=20, y=100): y/x = 100/20 = 5
Since the ratio of y to x is the same (5) for all pairs, y varies directly with x.
To find the constant of variation (k), we can take any of the ratios calculated above. Let's use the first pair (y=25, x=5):
k = y/x = 25/5 = 5
Therefore, the constant of variation (k) is 5.