For the data in the table, does y vary directly with x? If it does, find the constant of variation (k).
x-5
x-10
x-20
y-25
y-50
y-100
How can we figure this out
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.