The table shows the relationship “Mason rode 15 miles per hour on his bicycle.”
Hours (h)
Miles (m)
1
15
2
30
3
45
4
60
5
75
Which statements are correct? Check all that apply.
The variable m is the independent variable.
The number of miles increases as time increases.
The number of hours causes a change in the number of miles ridden.
The variable h is the independent variable.
The variable h is the dependent variable.
The farther Mason rides, the less time it takes.
The variable m is the dependent variable.
m = 15h
as h increases, so does m
and others
To determine which statements are correct, we need to understand the relationship between the variables in the table.
Explanation:
In the given table, the number of hours (h) represents the independent variable, and the number of miles (m) represents the dependent variable. The independent variable is the one that can be freely chosen or controlled, and in this case, the number of hours is chosen by Mason as it represents the time he spends riding his bicycle.
As Mason rides his bicycle, the number of miles he travels increases with time. Therefore, the statement "The number of miles increases as time increases" is correct. This is because the more time Mason spends riding, the farther he will travel.
While the number of hours (h) does cause a change in the number of miles (m) ridden, it is the dependent variable in this scenario. The statement "The variable h is the dependent variable" is incorrect.
Similarly, the statement "The variable m is the independent variable" is incorrect as the number of miles (m) depends on the number of hours (h).
The statement "The farther Mason rides, the less time it takes" cannot be determined from the given table. The table only provides information about the relationship between time and distance, but it does not provide information about the speed at which Mason rides or any change in speed.
Correct Statements:
- The number of miles increases as time increases.
- The number of hours causes a change in the number of miles ridden.
Therefore, the correct statements are the second and third statements.