hours miles
1/4 1
1/2 2
3/4 3
1 4
It takes Julian 1/2 an hour to walk 2 miles. He decides to start walking in his spare time, but because he wants to make sure he has enough time to go a desired distance he created the data table. At which point does the constant of proportionality appear?
A. (1 , 4)
B. (4 , 1)
C. ( 1 , 1/4)
D. (1/4 ,1)
The constant of proportionality appears in the table when the ratio of miles to hours remains the same. This occurs at every point in the table. However, to determine the exact point, we can calculate the ratio of miles to hours for each pair of values.
For the first pair, the ratio is 1 mile / 1/4 hour = 4 miles/hour.
For the second pair, the ratio is 2 miles / 1/2 hour = 4 miles/hour.
For the third pair, the ratio is 3 miles / 3/4 hour = 4 miles/hour.
For the fourth pair, the ratio is 4 miles / 1 hour = 4 miles/hour.
So, the constant of proportionality appears at every point in the table. Therefore, the correct option is:
A. (1 , 4)
hello bot
In this data table, the hours are on the left column and the miles are on the right column. The constant of proportionality for this data table represents the relationship between the hours and miles - how many miles can be walked in one hour.
To find the constant of proportionality, we need to look for where the ratio of miles to hours remains constant.
Looking at the data table, we can see that the ratio of miles to hours is constant at every row. The ratio is always 2 miles per 0.5 hours (or 4 miles per 1 hour).
Therefore, the constant of proportionality appears at the point (4, 1).
So, the answer is:
B. (4, 1)
To determine the constant of proportionality in this scenario, we need to find a consistent relationship between the hours it takes Julian to walk and the corresponding number of miles he covers. Looking at the given data table:
hours miles
1/4 1
1/2 2
3/4 3
1 4
We can see that as the number of hours increases, the number of miles also increases proportionally. In other words, there is a constant ratio between the number of hours and the number of miles. To identify this constant ratio, we can compare the values of miles to hours.
To do this, we can divide the number of miles by the number of hours for each data point:
1/4 ÷ 1 = 1/4
1/2 ÷ 2 = 1/4
3/4 ÷ 3 = 1/4
1 ÷ 4 = 1/4
Observing the results, we see that the ratio of miles to hours is consistently 1/4. This means that for every 1/4 hour, Julian walks 1 mile.
Now, let's look at the given options:
A. (1, 4)
B. (4, 1)
C. (1, 1/4)
D. (1/4, 1)
The constant of proportionality represents the ratio of miles to hours, which we determined earlier to be 1/4. Comparing this ratio to the options, we find that the correct answer is option D, (1/4, 1). This data point indicates that when Julian walks for 1/4 hour, he covers 1 mile.