الأسبوع 9 · المتغيران التابع والمستقل: العلاقات والقواعد · 3 دروس
1
Which quantity depends on which?
Discover Mathematics P6: Term 1, Unit 5, Lessons 1–2
GoalName the independent and the dependent variable in a situation and write the equation that links them.
New words
independent variable · the quantity we choose or change; the inputdependent variable · the quantity that changes because of the input; the outputrelationship · the rule that links two quantities
Explanation
Some quantities are linked: when one changes, the other changes too. The quantity we choose or change, such as time or the number of items, is the independent variable. The quantity that results from it, such as distance or cost, is the dependent variable, because it depends on the first. If oranges cost 15 LE for each kilogram, the cost c depends on the kilograms n we buy, so n is independent and c is dependent. The equation c = 15n links them. We can read it like a machine: put in n, multiply by 15, and out comes c.
Independent variable (input) n→Rule: multiply by 15→Dependent variable (output) c
Worked examples
Kilograms n
1
2
3
4
Cost c (LE)
15
30
45
60
Oranges cost 15 LE for each kg. The cost grows as the weight grows: c = 15n.
Hours t
1
2
3
Distance d (km)
60
120
180
A car drives 60 km each hour. After t hours it has gone d = 60t km. Time is the independent variable and distance is the dependent variable.
Situation
Independent
Dependent
Buying tickets
number of tickets
total price
Working
hours worked
wage
A square
length of a side
perimeter
Which depends on which? In each pair, ask: which one do we choose, and which one results?
Class activity
Dependent pairs. Look around your home and find three pairs of linked quantities, such as the number of eggs and the cost, or the minutes you walk and the distance. For each pair, say which one you choose (independent) and which one results (dependent). Write the rule in words.
Practice
1
A bakery earns money by selling loaves. Name the independent and the dependent variable.
Independent: the number of loaves sold. Dependent: the money earned.
2
You walk for some time and measure the distance. Which is independent?
The time is independent; the distance depends on it.
3
Pens cost 4 LE each. Write an equation for the cost c of n pens.
c = 4n.
4
A tap fills 5 litres every minute. Write an equation for the litres L after m minutes.
