Question

practice
in 1 - 8, identify the independent variable and the dependent variable
in each situation.

1. the number of hours, h, spent studying and
2. the length, l, of a pencil and the number

of times, t, it has been sharpened
the score, t, on a test

1. the length of a story in pages, p, and the
2. the number of students, s, ahead of you

number of words, w, in a story
in the lunch line and the time, t, it takes
you to get lunch

1. the amount of time, t, to finish a race and
2. tickets, t, sold for a race and the amount

of money, m, collected
the number of laps, l, around a track

1. the length, l, of a fence and the amount
2. the height, h, of a fence and the time,

t, it takes to climb the fence
of wood, w, to make the fence

1. write your own situation in which speed, s,
2. name at least two independent variables

is an independent variable.
that could result in a change in a monthly
cell phone bill.

1. critique reasoning you spend d dollars
2. the cost, c, of supplies for school depends

for g identical pairs of glasses. a friend claims
on other factors. list at least two
that because d increases if you increase g,
independent variables that could affect
the cost of school supplies.
and g increases if you increase d, either d or
g could be the independent variable. is your
friend correct? explain.

Explanation:

1. The number of hours spent studying (\(h\)) is the independent variable as it is the input that can be changed. The test score (\(t\)) is the dependent variable as it depends on the number of hours studied.
2. The number of times a pencil has been sharpened (\(t\)) is the independent variable. The length of the pencil (\(l\)) is the dependent variable as it is affected by the number of sharpenings.
3. The length of a story in pages (\(p\)) is the independent variable. The number of words (\(w\)) is the dependent variable as it depends on the number of pages.
4. The number of students ahead of you in the lunch line (\(s\)) is the independent variable. The time it takes to get lunch (\(t\)) is the dependent variable as it depends on the number of students ahead.
5. The number of laps around a track (\(l\)) is the independent variable. The amount of time to finish a race (\(t\)) is the dependent variable as it depends on the number of laps.
6. The number of tickets sold (\(t\)) is the independent variable. The amount of money collected (\(m\)) is the dependent variable as it depends on the number of tickets sold.
7. The length of a fence (\(l\)) is the independent variable. The amount of wood to make the fence (\(w\)) is the dependent variable as it depends on the length of the fence.
8. The height of a fence (\(h\)) is the independent variable. The time it takes to climb the fence (\(t\)) is the dependent variable as it depends on the height of the fence.
9. For example: The time \(t\) taken to travel a certain distance \(d\). Here, speed \(s\) is the independent variable (\(d = s\times t\)).
10. Two independent variables that could change a monthly cell - phone bill: The number of minutes of calls made (\(m\)), the amount of data used (\(d\)).
11. The friend is incorrect. The independent variable is the one that is deliberately changed. If you are buying glasses, the number of pairs \(g\) is the independent variable. The cost \(d\) is calculated as \(d = k\times g\) (where \(k\) is the cost per pair). You don't change the cost to change the number of pairs; you decide the number of pairs first (independent variable) and then the cost is determined (dependent variable).
12. Two independent variables that could affect the cost of school supplies: The number of notebooks bought (\(n\)), the price per notebook (\(p\)).

Answer:

1. Independent variable: \(h\) (number of hours spent studying), Dependent variable: \(t\) (test score)
2. Independent variable: \(t\) (number of times sharpened), Dependent variable: \(l\) (length of pencil)
3. Independent variable: \(p\) (length of story in pages), Dependent variable: \(w\) (number of words)
4. Independent variable: \(s\) (number of students ahead), Dependent variable: \(t\) (time to get lunch)
5. Independent variable: \(l\) (number of laps), Dependent variable: \(t\) (time to finish race)
6. Independent variable: \(t\) (tickets sold), Dependent variable: \(m\) (money collected)
7. Independent variable: \(l\) (length of fence), Dependent variable: \(w\) (amount of wood)
8. Independent variable: \(h\) (height of fence), Dependent variable: \(t\) (time to climb)
9. Example: Time \(t\) to travel distance \(d\) with speed \(s\) (\(d = s\times t\))
10. Number of call minutes (\(m\)), data used (\(d\))
11. Friend is incorrect. \(g\) (number of pairs) is independent, \(d\) (cost) is dependent (\(d = k\times g\))
12. Number of notebooks (\(n\)), price per notebook (\(p\))