Which set of values could be from a direct proportion?
1)
x | y
—|—
1/2 | 6
1 | 12
2 | 24
3 | 36
2)
x | y
—|—
0 | 0
1 | 1
2 | 4
3 | 6
3)
x | y
—|—
0 | 2
2 | 4
4 | 6
6 | 8
Which set of values could be from a direct proportion? 1) x | y 1/2 | 6 1 | 12 2 | 24 3 | 36 2) x | y 0 | 0 1 | 1 2 | 4 3 | 6 3) x | y 0 | 2 2 | 4 4 | 6 6 | 8
Share
To determine which set of values could be from a direct proportion, we need to check if the ratio ( frac{y}{x} ) is constant for each set.
1) For the first set:
– ( frac{6}{frac{1}{2}} = 12 )
– ( frac{12}{1} = 12 )
– ( frac{24}{2} = 12 )
– ( frac{36}{3} = 12 )
– Constant ratio: Yes (12). This set is a direct proportion.
2) For the second set:
– ( frac{0}{0} ) is undefined, but let’s check the rest:
– ( frac{1}{1} = 1 )
– ( frac{4}{2} = 2 )
– ( frac{6}{3} = 2 )
– Constant ratio: No. This set is not a direct proportion.
3) For the third set:
– ( frac{2}{0} ) is undefined.
– ( frac{4}{2} = 2 )
– ( frac{6}{4} = 1.5 )
– ( frac{8}{6} approx 1.33 )
– Constant ratio: No.