# Introduction to Graphs - Class 8 - Mathematics

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## Examples - Introduction to Graphs | NCERT | Mathematics | Class 8

**(A graph on "performance")**

The given graph (Fig 13.3) represents the total runs scored by two batsmen A and B, during each of the ten different matches in the year 2007. Study the graph and answer the following questions.

(i) What information is given on the two axes?

(ii) Which line shows the runs scored by batsman A?

(iii) Were the run scored by them same in any match in 2007 ? If so, in which match?

(iii) Among the two batsmen, who is steadier? How do you judge it?

Let's analyze the given data and provide answers to your questions based on the data for Batsman A and B in ten matches:

(i) **What information is given on the two axes?**

On the horizontal axis (X-axis), we have the "Match number" ranging from 1 to 10, representing each of the ten different matches played in the year 2007.

On the vertical axis (Y-axis), we have the "Runs scored" by each batsman in each match.

(ii) **Which line shows the runs scored by batsman A?**

The dashed line refers to batsman A.

(iii) **Were the runs scored by them the same in any match in 2007? If so, in which match?**

Yes, in Match 4, both Batsman A and Batsman B scored exactly 60 runs.

(iv) **Among the two batsmen, who is steadier? How do you judge it?**

To determine who is steadier, we compare the consistency in their performance across all matches. A steadier batsman would show less variation in the number of runs scored across different matches.

Looking at the scores:

Batsman A had scores of 20, 115, 0, 60, 20, 90, 35, 75, 0, 45. The variation includes scores from 0 to 115 runs, showing significant inconsistency.

Batsman B scored 60, 40, 50, 60, 45, 45, 100, 60, 50, 55. Though there is variation, the scores are more clustered around the middle values, and there are no extreme lows like Batsman A.

Based on this, **Batsman B** is steadier because the scores vary less from match to match compared to Batsman A, revealing a more consistent performance.

The given graph (Fig 13.4) describes the distances of a car from a city $\mathrm{P}$ at different times when it is travelling from City P to City Q, which are $350 \mathrm{~km}$ apart. Study the graph and answer the following:

(i) What information is given on the two axes?

(ii) From where and when did the car begin its journey?

(iii) How far did the car go in the first hour?

(iv) How far did the car go during (i) the 2nd hour? (ii) the 3rd hour?

(v) Was the speed same during the first three hours? How do you know it?

(vi) Did the car stop for some duration at any place? Justify your answer.

(vii) When did the car reach City Q?

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Sign up now**(Quantity and Cost)**

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.

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Sign up now**(Principal and Simple Interest)**

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 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 .

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Sign up now(Time and Distance)

Ajit can ride a scooter constantly at a speed of $30 \mathrm{kms} / \mathrm{hour}$. Draw a time-distance graph for this situation. Use it to find

(i) the time taken by Ajit to ride $75 \mathrm{~km}$. (ii) the distance covered by Ajit in $3 \frac{1}{2}$ hours.

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## Exercise 13.1 - Introduction to Graphs | NCERT | Mathematics | Class 8

The following graph shows the temperature of a patient in a hospital, recorded every hour.

(a) What was the patient's temperature at 1 p.m. ?

(b) When was the patient's temperature $38.5^{\circ} \mathrm{C}$ ?

(c) The patient's temperature was the same two times during the period given. What were these two times?

(d) What was the temperature at 1.30 p.m.? How did you arrive at your answer?

(e) During which periods did the patients' temperature showed an upward trend?

Given the data for the patient's temperature recorded every hour, we can address the queries as follows:

### (a) What was the patient's temperature at 1 p.m. ?

The patient's temperature at 1 p.m. was $36.5^{\circ}\mathrm{C}$.

### (b) When was the patient's temperature $38.5^{\circ} \mathrm{C}$ ?

The patient's temperature was $38.5^{\circ} \mathrm{C}$ at 12 noon.

### (c) The patient's temperature was the same two times during the period given. What were these two times?

The patient's temperature was the same at 1 p.m. and 2 p.m., both times it was $36.5^{\circ}\mathrm{C}$.

### (d) What was the temperature at 1.30 p.m.? How did you arrive at your answer?

The patient's temperature at 1.30 p.m. can be estimated by considering the trend between 1 p.m. ($36.5^{\circ} \mathrm{C}$) and 2 p.m. ($36.5^{\circ} \mathrm{C}$).

Since the temperature remained the same between these times, it can be inferred that at 1.30 p.m., the temperature was also $36.5^{\circ} \mathrm{C}$.

### (e) During which periods did the patients' temperature showed an upward trend?

Analyzing the data:

From 9 a.m. to 11 a.m., the temperature showed an upward trend, going from $35.5^{\circ}\mathrm{C}$ to $39^{\circ}\mathrm{C}$.

From 2 p.m. to 3 p.m., the temperature increased from $36.5^{\circ}\mathrm{C}$ to $37^{\circ}\mathrm{C}$.

Therefore, the periods of upward trend were 9 a.m. to 11 a.m. and 2 p.m. to 3 p.m.

The following line graph shows the yearly sales figures for a manufacturing company.

(a) What were the sales in (i) 2002 (ii) 2006?

(b) What were the sales in (i) 2003 (ii) 2005 ?

(c) Compute the difference between the sales in 2002 and 2006.

(d) In which year was there the greatest difference between the sales as compared to its previous year?

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For an experiment in Botany, two different plants, plant $\mathrm{A}$ and plant $\mathrm{B}$ were grown under similar laboratory conditions. Their heights were measured at the end of each week for 3 weeks. The results are shown by the following graph.

(a) How high was Plant A after (i) 2 weeks (ii) 3 weeks?

(b) How high was Plant B after (i) 2 weeks (ii) 3 weeks?

(c) How much did Plant A grow during the 3rd week?

(d) How much did Plant B grow from the end of the 2nd week to the end of the 3rd week?

(e) During which week did Plant A grow most?

(f) During which week did Plant B grow least?

(g) Were the two plants of the same height during any week shown here? Specify.

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The following graph shows the temperature forecast and the actual temperature for each day of a week.

(a) On which days was the forecast temperature the same as the actual temperature?

(b) What was the maximum forecast temperature during the week?

(c) What was the minimum actual temperature during the week?

(d) On which day did the actual temperature differ the most from the forecast temperature?

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Use the tables below to draw linear graphs.

(a) The number of days a hill side city received snow in different years.

Year | 2003 | 2004 | 2005 | 2006 |
---|---|---|---|---|

Days | 8 | 10 | 5 | 12 |

(b) Population (in thousands) of men and women in a village in different years.

Year | 2003 | 2004 | 2005 | 2006 | 2007 |
---|---|---|---|---|---|

Number of Men | 12 | 12.5 | 13 | 13.2 | 13.5 |

Number of Women | 11.3 | 11.9 | 13 | 13.6 | 12.8 |

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A courier-person cycles from a town to a neighbouring suburban area to deliver a parcel to a merchant. His distance from the town at different times is shown by the following graph.

(a) What is the scale taken for the time axis?

(b) How much time did the person take for the travel?

(c) How far is the place of the merchant from the town?

(d) Did the person stop on his way? Explain.

(e) During which period did he ride fastest?

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Can there be a time-temperature graph as follows? Justify your answer.

(i)

(ii)

(iii)

(iv)

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## Exercise 13.2 - Introduction to Graphs | NCERT | Mathematics | Class 8

Draw the graphs for the following tables of values, with suitable scales on the axes.

Cost of apples

Number of apples | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

Cost in ₹ | 5 | 10 | 15 | 20 | 25 |

Here is the graph for the cost of apples based on the given table of values:

This graph has been plotted with the number of apples on the x-axis and the cost in ₹ on the y-axis, accurately representing the information from your table.

Draw the graphs for the following tables of values, with suitable scales on the axes.

Distance travelled by a car

Time (in hours) | 6 a.m | 7 a.m | 8 a.m | 9 a.m |
---|---|---|---|---|

Distances (in km) | 40 | 80 | 120 | 160 |

(i) How much distance did the car cover during the period 7.30 a.m. to 8 a.m?

(ii) What was the time when the car had covered a distance of $100 \mathrm{~km}$ since it's start?

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Draw the graphs for the following tables of values, with suitable scales on the axes.

Interest on deposits for a year.

Deposit (in ₹) | 1000 | 2000 | 3000 | 4000 | 5000 |
---|---|---|---|---|---|

Simple Interest (in ₹) | 80 | 160 | 240 | 320 | 400 |

(i) Does the graph pass through the origin?

(ii) Use the graph to find the interest on ₹ 2500 for a year.

(iii) To get an interest of ₹ 280 per year, how much money should be deposited?

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Draw a graph for the following.

Side of square (in cm) | 2 | 3 | 3.5 | 5 | 6 |
---|---|---|---|---|---|

Perimeter (in cm) | 8 | 12 | 14 | 20 | 24 |

Is it a linear graph?

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Draw a graph for the following.

Side of square (in cm) | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|

Area (in $\mathbf{c m}^{2}$ ) | 4 | 9 | 16 | 25 | 36 |

Is it a linear graph?

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## Extra Questions - Introduction to Graphs | NCERT | Mathematics | Class 8

The points $(5,-2)$ and $(-2,-5)$ lie in:

A. the same quadrant

B. II and III quadrants, respectively

C. II and IV quadrants, respectively

D. IV and III quadrants, respectively

We determine in which quadrants the points $(5,-2)$ and $(-2,-5)$ lie:

The first point $(5, -2)$ has a positive $x$-coordinate and a negative $y$-coordinate. This placement is characteristic of the

**IV quadrant**.The second point $(-2, -5)$, however, has a negative $x$-coordinate and a negative $y$-coordinate, which is typical of the

**III quadrant**.

Therefore, the correct option is **D**: the points $(5,-2)$ and $(-2,-5)$ lie in the **IV and III quadrants**, respectively.

Less than ogive is a

A) Non-increasing graph

B) Non-decreasing graph

C) Decreasing graph

D) Increasing graph