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Some Application of Linear Graphs

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Topics

description

  • Independent variable
  • Dependent variable
  • Quantity and Cost
  • Principal and Simple Interest
  • Time and Distance

definition

  • Independent Variable: Anything which is completely independent and its quantity do not depend on any other factor then it is called Independent Variable.

  • Dependent Variable: Anything which increases or decreases with the quantity of any other factor or it is dependent on any other factor then it is called Dependent Variable.

notes

Some Applications:

  • Independent Variable: Anything which is completely independent and its quantity do not depend on any other factor then it is called Independent Variable.

  • Dependent Variable: Anything which increases or decreases with the quantity of any other factor or it is dependent on any other factor then it is called a Dependent Variable.

  • For example, If more electricity is consumed, the bill is bound to be high. The amount of electric bill depends on the quantity of electricity used. We say that the quantity of electricity is an independent variable (or sometimes control variable) and the amount of electric bill is the dependent variable.

  • The relation between the dependent variable and the independent variable is shown through a graph.

For example, 
The following table gives the quantity of petrol and its cost.

No. of Litres of petrol 10 15 20 25
Cost of petrol in ₹ 500 750 1000 1250

Plot a graph to show the data.

Solution:

  1. Let us take a suitable scale on both the axes.
  2. Mark the number of litres along the horizontal axis.
  3. Mark cost of petrol along the vertical axis.
  4. Plot the points: (10,500), (15,750), (20,1000), (25,1250).
  5. Join the points.

Example

A bank gives 10% Simple Interest (S.I.) on deposits by senior citizens. Draw a graph to illustrate the relation between the sum deposited and the simple interest earned. Find from your graph
(a) the annual interest obtainable for an investment of ₹ 250.
(b) the investment one has to make to get an annual simple interest of ₹ 70.
Sum deposited Simple interest for a year
₹ 100 ₹ `(100 xx 1 xx 10)/100` = ₹ 10
₹ 200 ₹ `(200 xx 1 xx 10)/100` = ₹ 20
₹ 300 ₹ `(300 xx 1 xx 10)/100` = ₹ 30
₹ 500 ₹ `(500 xx 1 xx 10)/100` = ₹ 50
₹ 1000 ₹ 100
We get a table of values.
Deposit (in ₹) 100 200 300 500 1000
Annual S.I. (in ₹) 10 20 30 50 100
(i) Scale : 1 unit = ₹ 100 on horizontal axis; 1 unit = ₹ 10 on vertical axis.
(ii) Mark Deposits along the horizontal axis.
(iii) Mark Simple Interest along the vertical axis.
(iv) Plot the points : (100,10), (200, 20), (300, 30), (500,50) etc.
(v) Join the points. We get a graph that is a line.
  1. Corresponding to ₹ 250 on the horizontal axis, we get the interest to be ₹ 25 on the vertical axis.
  2. Corresponding to ₹ 70 on the vertical axis, we get the sum to be ₹ 700 on the horizontal axis.

Example

Ajit can ride a scooter constantly at a speed of 30 kms/hour. Draw a time-distance graph for this situation. Use it to find
(i) the time taken by Ajit to ride 75 km.
(ii) the distance covered by Ajit in `3 1/2` hours.
Hours of ride Distance covered
1 hour 30 km
2 hours 2 × 30 km = 60 km
3 hours 3 × 30 km = 90 km
4 hours 4 × 30 km = 120 km and so on.
We get a table of values.
Time (in hours) 1 2 3 4
Distance covered (in km) 30 60 90 120
(i) Scale:
Horizontal: 2
units = 1 hour
Vertical: 1 unit = 10 km
(ii) Mark time on horizontal axis.
(iii) Mark distance on vertical axis.
(iv) Plot the points: (1, 30), (2, 60), (3, 90), (4, 120).
(v) Join the points. We get a linear graph.
(a) Corresponding to 75 km on the vertical axis, we get the time to be 2.5 hours on the horizontal axis. Thus 2.5 hours are needed to cover 75 km.
(b) Corresponding to `3 1/2` hours on the horizontal axis, the distance covered is 105 km on the vertical axis.
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