Class 8 Maths Notes for Introduction To Graphs
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Page 1
NOTES
CLASS 8
MATHS
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CLASS 8
MATHS
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Page 2
INTRODUCTIN TO GRAPHS
I. IMPORTANT CONCEPTS / RESULTS:
I. A line graph displays data that changes continuously over periods of time.
II. A line graph which is a whole unbroken line is called a linear graph.
III. The horizontal line is called the x-axis and the vertical line is called the y-axis.
IV. Independent variable (or sometimes control variable) and Dependent variable.
V. Some Applications :
a. Quantity and Cost
b. Principal and Simple Interest
c. Time and Distance
II. EXAMPLES AND ILLUSTRATIONS:
1. Every point on the y axis is of the form.
(a) (0, y) (b) (x, 0)
(c) (x, y) (d) (x, 1)
Solution: The correct answer is (a).
2. The given graph shows Amar‘s trip to an exhibition by a car. Observe the graph carefully and find what
was he doing between 5 pm and 7 pm?
(a) Driving to the mall.
(b) Driving back home.
(c) Was not driving.
(d) Not enough data to answer.
Solution : The correct answer is (c).
3. The coordinates of a point at a distance of 3 units from the x axis and 6 units from the y axis is
(a) (0, 3) (b) (6, 0) (c) (3, 6) (d) (6, 3)
Solution : The correct answer is (c).
4. The point (3, 4) is at a distance of
(a) 3 from both the axis (b) 4 from both the axis
(c) 4 from the x axis and 3 from y axis (d) 3 from x axis and 4 from y axis
Solution : The correct answer is (d).
5. Plot the following points on a graph sheet. Verify if they lie on a line
(a) A(4, 0), B(4, 2), C(4, 6), D(4, 2.5)
(b) P(1, 1), Q(2, 2), R(3, 3), S(4, 4)
(c) K(2, 3), 145, 3), M(5, 5), N(2, 5).
Solution :Draw the x-axis and y-axls. Plot the points A (4,0), B (4. 2), C (4, 6) and D (4, 2.5) as
shown.
Clearly, these points lie on a line ABDC.
75
I. IMPORTANT CONCEPTS / RESULTS:
I. A line graph displays data that changes continuously over periods of time.
II. A line graph which is a whole unbroken line is called a linear graph.
III. The horizontal line is called the x-axis and the vertical line is called the y-axis.
IV. Independent variable (or sometimes control variable) and Dependent variable.
V. Some Applications :
a. Quantity and Cost
b. Principal and Simple Interest
c. Time and Distance
II. EXAMPLES AND ILLUSTRATIONS:
1. Every point on the y axis is of the form.
(a) (0, y) (b) (x, 0)
(c) (x, y) (d) (x, 1)
Solution: The correct answer is (a).
2. The given graph shows Amar‘s trip to an exhibition by a car. Observe the graph carefully and find what
was he doing between 5 pm and 7 pm?
(a) Driving to the mall.
(b) Driving back home.
(c) Was not driving.
(d) Not enough data to answer.
Solution : The correct answer is (c).
3. The coordinates of a point at a distance of 3 units from the x axis and 6 units from the y axis is
(a) (0, 3) (b) (6, 0) (c) (3, 6) (d) (6, 3)
Solution : The correct answer is (c).
4. The point (3, 4) is at a distance of
(a) 3 from both the axis (b) 4 from both the axis
(c) 4 from the x axis and 3 from y axis (d) 3 from x axis and 4 from y axis
Solution : The correct answer is (d).
5. Plot the following points on a graph sheet. Verify if they lie on a line
(a) A(4, 0), B(4, 2), C(4, 6), D(4, 2.5)
(b) P(1, 1), Q(2, 2), R(3, 3), S(4, 4)
(c) K(2, 3), 145, 3), M(5, 5), N(2, 5).
Solution :Draw the x-axis and y-axls. Plot the points A (4,0), B (4. 2), C (4, 6) and D (4, 2.5) as
shown.
Clearly, these points lie on a line ABDC.
75
Page 3
6. Write the coordinates of the vertices of each of the figures given below.
Solution :Clearly, from the graph the coordinates of points are:
O (0, 0), A (2, 0), B (2, 3) and C (0, 3);
P (4, 3), Q (6, 1), R (6, 5) and S (4, 7);
L (7, 7), M (10, 8) and K (10, 5).
7. Plot the point (4, 3) on a graph sheet. Is it the same as the point (3, 4)?
Solution: Locate the x, y axes, (they are actually number lines!). Start at O (0, 0). Move 4 units to the
right; then move 3 units up, you reach the point (4, 3). From Fig 15.13, you can see that the points (3, 4)
and (4, 3) are two different points.
8. Draw the graphs for the following tables of values, with suitable scales on the axes.
Distance travelled by a car:
(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 km since it‘s start?
Solution: 1) 20km
2) 7:30am
9. Draw a graphs for the following. Is it a linear graph?
76
Solution :Clearly, from the graph the coordinates of points are:
O (0, 0), A (2, 0), B (2, 3) and C (0, 3);
P (4, 3), Q (6, 1), R (6, 5) and S (4, 7);
L (7, 7), M (10, 8) and K (10, 5).
7. Plot the point (4, 3) on a graph sheet. Is it the same as the point (3, 4)?
Solution: Locate the x, y axes, (they are actually number lines!). Start at O (0, 0). Move 4 units to the
right; then move 3 units up, you reach the point (4, 3). From Fig 15.13, you can see that the points (3, 4)
and (4, 3) are two different points.
8. Draw the graphs for the following tables of values, with suitable scales on the axes.
Distance travelled by a car:
(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 km since it‘s start?
Solution: 1) 20km
2) 7:30am
9. Draw a graphs for the following. Is it a linear graph?
76
Page 4
Solution: Plot points (2, 4), (3, 9), (4, 16), (5, 25), (6,36) It is not a linear graph.
III. QUESTIONS FOR PRACTICE:
1. (o, y) are the co-ordinates of a point lying on which of the following?
(i) origin (ii) x-axis (iii) y-axis (iv) none of these.
2. The point (3, 2) is nearer to:
(i) x-axis (ii) y-axis (iii) origin (iv) none of these.
3. The point (–5, 6) is nearer it:
(i) x-axis (ii) y-axis (iii) origin (iv) none of these.
4. The point (–3, –3) is
(i) nearer to x-axis (ii) y-axis
(iii) near to origin (iv)equidistant from x-axis and y-axis.
5. The point (0, 4) lies on which of the following:
(i) x-axis (ii) y-oxis (iii) origin (iv) none of these.
6. The point (–3, 0) livs on which of the following?
(i) x-axis (ii) y-oxis (iii) origin (iv) none of these.
7. The poits (–3, 2) and (2 , –3) represent:
(i) different points(ii) same point (iii) the origin
(iv) none of these.
8. By joining (–1, –1), (0, 0) and (3, 3) represent:
(i) a triangle (ii) a curved line
(iii) a straight line passing through origin
(iv) a straight line not passing through origin.
9. By joining (–3 , 2) , (–3 , –3) and (–3, 4), which of the following is obtained?
(i) a triangle (ii) A straight line not passing through origin
(iii) A straight line passing through origin(iv) none of these.
10. Which of the following points lies on y-axis?
(i) (–4 , 0) (ii) (4 ,0) (iii) (0 , –4) (iv)(–4 , 4)
Answers :
77
III. QUESTIONS FOR PRACTICE:
1. (o, y) are the co-ordinates of a point lying on which of the following?
(i) origin (ii) x-axis (iii) y-axis (iv) none of these.
2. The point (3, 2) is nearer to:
(i) x-axis (ii) y-axis (iii) origin (iv) none of these.
3. The point (–5, 6) is nearer it:
(i) x-axis (ii) y-axis (iii) origin (iv) none of these.
4. The point (–3, –3) is
(i) nearer to x-axis (ii) y-axis
(iii) near to origin (iv)equidistant from x-axis and y-axis.
5. The point (0, 4) lies on which of the following:
(i) x-axis (ii) y-oxis (iii) origin (iv) none of these.
6. The point (–3, 0) livs on which of the following?
(i) x-axis (ii) y-oxis (iii) origin (iv) none of these.
7. The poits (–3, 2) and (2 , –3) represent:
(i) different points(ii) same point (iii) the origin
(iv) none of these.
8. By joining (–1, –1), (0, 0) and (3, 3) represent:
(i) a triangle (ii) a curved line
(iii) a straight line passing through origin
(iv) a straight line not passing through origin.
9. By joining (–3 , 2) , (–3 , –3) and (–3, 4), which of the following is obtained?
(i) a triangle (ii) A straight line not passing through origin
(iii) A straight line passing through origin(iv) none of these.
10. Which of the following points lies on y-axis?
(i) (–4 , 0) (ii) (4 ,0) (iii) (0 , –4) (iv)(–4 , 4)
Answers :
77
Page 5
1)ii 2)i 3)ii 4)iv 5)ii
6)i 7)i 8)iii 9)ii 10)iii
CHAPTER TEST – I
MAX.MARKS: 20 TIME: 35MIN
I. Choose the correct answer. (4 × 1M = 4M)
1. A graph that displays data that changes continuously over periods of time is
(a) bar graph (b) pie chart (c) histogram (d) line graph
2. A point which lies on both the axis is __________
(a) (0, 0) (b) (0, 1) (c) (1, 0) (d) (1, 1)
3. In the given graph the letter that indicates the point (0, 3) is
(a) P (b) Q (c) R (d) S
4. In the given figure the position of the book on the table may be given by
(a) (7, 3) (b) (3, 7) (c) (3, 3) (d) (7, 7)
II. Answer the following questions. (3 × 2M = 6M)
5. If y–coordinate is 3 times x -coordinate, form a table for it.(atleast 2 points)
6. Plot the given points on a graph sheet.
(a) (5, 4) (b) (2, 0) (c) (3, 1) (d) (0, 4)
7. Complete the given tables and draw a graph for each.
78
6)i 7)i 8)iii 9)ii 10)iii
CHAPTER TEST – I
MAX.MARKS: 20 TIME: 35MIN
I. Choose the correct answer. (4 × 1M = 4M)
1. A graph that displays data that changes continuously over periods of time is
(a) bar graph (b) pie chart (c) histogram (d) line graph
2. A point which lies on both the axis is __________
(a) (0, 0) (b) (0, 1) (c) (1, 0) (d) (1, 1)
3. In the given graph the letter that indicates the point (0, 3) is
(a) P (b) Q (c) R (d) S
4. In the given figure the position of the book on the table may be given by
(a) (7, 3) (b) (3, 7) (c) (3, 3) (d) (7, 7)
II. Answer the following questions. (3 × 2M = 6M)
5. If y–coordinate is 3 times x -coordinate, form a table for it.(atleast 2 points)
6. Plot the given points on a graph sheet.
(a) (5, 4) (b) (2, 0) (c) (3, 1) (d) (0, 4)
7. Complete the given tables and draw a graph for each.
78
Page 6
III. Answer the following questions. (2 × 3M = 6M)
8. The cost of a note book is Rs 10. Draw a graph after making a table showing cost of 2, 3, 4, .... note
books. Use it to find
(a) the cost of 7 notebooks.
(b) The number of note books that can be purchased with Rs 50.
9. Explain the situations represented by the following distance-time graphs.
IV. CASE STUDY: A biology teacher teaching Botany to her class VIII students and explaining them about
the growth of plants. To make it more exciting, she took two different plants, plant A and plant B and
were grown under similar laboratory conditions. The students were asked to measure their heights at the
end of each week for 3 weeks. The results are shown by the following graph. (4M)
Answer the following based on your observations:
1. How high was Plant A after 2 weeks? 1M
2. How high was Plant B after 3 weeks? 1M
3. Were the two plants of the same height during any week shown here? Specify. 1M
4. How much did Plant B grow from the end of the 2nd week to the end of the3rd week? 1M
CHAPTER TEST – II
MAX.MARKS: 30 TIME: 60MIN
I. Choose the correct answer. (5 × 1M = 5M)
79
8. The cost of a note book is Rs 10. Draw a graph after making a table showing cost of 2, 3, 4, .... note
books. Use it to find
(a) the cost of 7 notebooks.
(b) The number of note books that can be purchased with Rs 50.
9. Explain the situations represented by the following distance-time graphs.
IV. CASE STUDY: A biology teacher teaching Botany to her class VIII students and explaining them about
the growth of plants. To make it more exciting, she took two different plants, plant A and plant B and
were grown under similar laboratory conditions. The students were asked to measure their heights at the
end of each week for 3 weeks. The results are shown by the following graph. (4M)
Answer the following based on your observations:
1. How high was Plant A after 2 weeks? 1M
2. How high was Plant B after 3 weeks? 1M
3. Were the two plants of the same height during any week shown here? Specify. 1M
4. How much did Plant B grow from the end of the 2nd week to the end of the3rd week? 1M
CHAPTER TEST – II
MAX.MARKS: 30 TIME: 60MIN
I. Choose the correct answer. (5 × 1M = 5M)
79
Page 7
1. A graph that displays data that changes continuously over periods of time is
(a) bar graph (b) pie chart (c) histogram (d) line graph
2. A point which lies on the y – axis only is __________
(a) (0, 0) (b) (0, 1) (c) (1, 0) (d) (1, 1)
3. In the given graph the letter S indicates the point……….
(a) (3, 0) (b) (0, 3) (c) (0, 0) (d) (3, 3)
4. In the given figure the position of the book on the table may be given by
(a) (7, 3) (b) (3, 7) (c) (3, 3) (d) (7, 7)
5. Data was collected on a student‘s typing rate and graph was drawn as shown below. Approximately how
many words had this student typed in 30 seconds?
(a) 20 (b) 24 (c) 28 (d) 34
II. Answer the following questions. (4 × 2M = 8M)
6. Make a line graph for the area of a square as per the given table. Is it a linear graph?
80
(a) bar graph (b) pie chart (c) histogram (d) line graph
2. A point which lies on the y – axis only is __________
(a) (0, 0) (b) (0, 1) (c) (1, 0) (d) (1, 1)
3. In the given graph the letter S indicates the point……….
(a) (3, 0) (b) (0, 3) (c) (0, 0) (d) (3, 3)
4. In the given figure the position of the book on the table may be given by
(a) (7, 3) (b) (3, 7) (c) (3, 3) (d) (7, 7)
5. Data was collected on a student‘s typing rate and graph was drawn as shown below. Approximately how
many words had this student typed in 30 seconds?
(a) 20 (b) 24 (c) 28 (d) 34
II. Answer the following questions. (4 × 2M = 8M)
6. Make a line graph for the area of a square as per the given table. Is it a linear graph?
80
Page 8
7. If x–coordinate is 2 times y -coordinate, form a table for it.(atleast 2 points)
8. Plot the given points on a graph sheet and find the shape.
(5, 4) (2, 0) (3, 1) (0, 4)
9. Complete the given tables and draw a graph for each.
III. Answer the following questions. (3 × 3M = 9M)
10. The cost of a note book is Rs 10. Draw a graph after making a table showing cost of 2, 3, 4, .... note
books. Use it to find
(a) the cost of 7 notebooks.
(b) The number of note books that can be purchased with Rs 50.
11. Explain the situations represented by the following distance-time graphs.
12. Draw the graph for the Distance travelled by a car with suitable scales on the axes and Find , how much
distance did the car cover during the period 7.30 a.m. to 8 a.m?
IV. CASE STUDY- I: Amar and Ravi went to a Chocolate making company with their maths teacher for a
visit. When they were going around in the company they observed a graph projected on a wall which
shows the yearly sales of the company. Their maths teacher was explaining the graph to them. Then he
asked few questions. Please help Amar and Ravi in answering th equestions.
(4M)
81
8. Plot the given points on a graph sheet and find the shape.
(5, 4) (2, 0) (3, 1) (0, 4)
9. Complete the given tables and draw a graph for each.
III. Answer the following questions. (3 × 3M = 9M)
10. The cost of a note book is Rs 10. Draw a graph after making a table showing cost of 2, 3, 4, .... note
books. Use it to find
(a) the cost of 7 notebooks.
(b) The number of note books that can be purchased with Rs 50.
11. Explain the situations represented by the following distance-time graphs.
12. Draw the graph for the Distance travelled by a car with suitable scales on the axes and Find , how much
distance did the car cover during the period 7.30 a.m. to 8 a.m?
IV. CASE STUDY- I: Amar and Ravi went to a Chocolate making company with their maths teacher for a
visit. When they were going around in the company they observed a graph projected on a wall which
shows the yearly sales of the company. Their maths teacher was explaining the graph to them. Then he
asked few questions. Please help Amar and Ravi in answering th equestions.
(4M)
81
Page 9
Answer the following based on your observations:
1. What were the sales in (i) 2002 (ii) 2006? 1M
2. What were the sales in (i) 2003 (ii) 2005? 1M
3. In which year was there the greatest difference between the sales as compared to its previous year?
1M
V. CASE STUDY- II: Study the graph given below of a person who started from his home and returned at
the end of the day. Answer the questions that follow. (4M)
At what time did he cover 16 km of his journey? 1M
1. What was he doing from 3 pm to 5 pm? 1M
2. Calculate the average speed of the man from (a) A to B (b) B to C 2M
82
1. What were the sales in (i) 2002 (ii) 2006? 1M
2. What were the sales in (i) 2003 (ii) 2005? 1M
3. In which year was there the greatest difference between the sales as compared to its previous year?
1M
V. CASE STUDY- II: Study the graph given below of a person who started from his home and returned at
the end of the day. Answer the questions that follow. (4M)
At what time did he cover 16 km of his journey? 1M
1. What was he doing from 3 pm to 5 pm? 1M
2. Calculate the average speed of the man from (a) A to B (b) B to C 2M
82
Page 10
Study Materials
Notes
Model Papers Class 6 Notes
Sample Papers Class 7 Notes
Half Yearly Sample Papers Class 8 Notes
Class 9 Notes
Important Resources
Class 10 Notes
Periodic Table
Class 11 Notes
Writing Skills / Formats
Maps of India / World Class 12 Notes
Books and Solutions
NCERT Books
NCERT Book Solutions
HC Verma Chapter Wise Solutions
RD Sharma Solutions
CGBSE Solutions
Notes
Model Papers Class 6 Notes
Sample Papers Class 7 Notes
Half Yearly Sample Papers Class 8 Notes
Class 9 Notes
Important Resources
Class 10 Notes
Periodic Table
Class 11 Notes
Writing Skills / Formats
Maps of India / World Class 12 Notes
Books and Solutions
NCERT Books
NCERT Book Solutions
HC Verma Chapter Wise Solutions
RD Sharma Solutions
CGBSE Solutions
Document Details
| Board / Org | Aglasem |
| Exam | Class 8 |
| Type | Notes |
| Pages | 10 |
| Language | english |
| Updated | 24 Sep 2026 |