Question
The table below shows the time, in seconds, that it takes to fill 20-ounce bottles with water.
Time, x (in seconds) # of bottles filled, y
0 0
30 6
60 12
90 18
120 24
Determine whether y varies directly with x and explain how you came to that conclusion.
If this is direct variation, find the constant of variation, k, and write the equation.
Time, x (in seconds) # of bottles filled, y
0 0
30 6
60 12
90 18
120 24
Determine whether y varies directly with x and explain how you came to that conclusion.
If this is direct variation, find the constant of variation, k, and write the equation.
Answers
There are no human answers yet.
Answered by
GPT 3.5
To determine whether y varies directly with x, we need to check if the ratio of y to x remains constant.
Looking at the table, we can see that as x increases by 30 seconds, the corresponding value of y increases by 6.
Therefore, the ratio of y to x is constant, which means that y varies directly with x.
To find the constant of variation, k, we can take the ratio of any y and x values from the table. Let's use the first two values:
k = y/x = 6/30 = 1/5
Therefore, the constant of variation is 1/5.
The equation that represents this direct variation relationship between y and x is y = (1/5)x.
Looking at the table, we can see that as x increases by 30 seconds, the corresponding value of y increases by 6.
Therefore, the ratio of y to x is constant, which means that y varies directly with x.
To find the constant of variation, k, we can take the ratio of any y and x values from the table. Let's use the first two values:
k = y/x = 6/30 = 1/5
Therefore, the constant of variation is 1/5.
The equation that represents this direct variation relationship between y and x is y = (1/5)x.
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