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Introduction to Graphs

Long Answer Type

11. Following graph describes the distance of a car from a city-P to city-Q, which are 350 km apart. Study the graph and answer the following questions.

(a) What information is given on the two axes?
(b) From where and when did the car begin its journey?
(c) How far did the car go in the first hour?
(d) How far did the car go during (i) the 2^nd hour? (ii) the 3^rd hour?
(e) Was the speed same during the first three hours? How do you know it?
(f) Did the car stop for some duration at any place? Justify your answer.
(g) When did the car reach City Q?

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12.

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), L(5, 3), M(5, 5), N(2, 5)

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Short Answer Type

13. Draw the line passing through (2, 3) and (3, 2). Find the coordinates of the points at which this line meets the x-axis and y-axis.

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14. Write the coordinates of the vertices of each of these adjoining Figures.

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True Or False

15. State whether True or False. Correct that are false.

A point whose x coordinate is zero and y-coordinate is non-zero will lie on the y-axis.

A point whose y coordinate is zero and x-coordinate is 5 will lie on y-axis.

The coordinates of the origin are (0, 0).

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Short Answer Type

16. The number of litres of petrol you buy to fill a car’s petrol tank will decide the amount you have to pay. Which is the independent variable here? Think about it.

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17. The following table gives the quantity of petrol and its cost.

Plot a graph to show the data.
Use the graph to find how much petrol can be purchased for Rs 800.

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

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19. 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?

Steps:
I. Draw the axis.
II. Choose suitable scale along x-axis and along y-axis.
III.Mark time (in hours) along x-axis and distance (in km) along y-axis
IV.Plot the points (6, 40) (7, 80), (8, 120) and (9, 160).
V. By joining the points we get the required graph.

(i) In the graph, draw a perpendicular at the point indicating 7:30 a.m. on the x-axis such that it meets the graph at A. From A draw a line parallel to x-axis to meet y-axis at 100 km.
∴ Distance travelled between 7:30 a.m. and 8:00 a.m.
= 120 km – 100 km
= 20 km

(ii) 7:30 a.m.
Steps:I. Draw the axis.II. Choose suitable scale along x-axis and a

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20. Draw the graphs for the following tables of values, with suitable scales on the axes,
Interest on deposits for a year.

(i) Does the graph pass through the origin?
(ii) Use the graph to find the interest on Rs 2500 for a year.
(iii) To get an interest of Rs 280 per year, how much money should be deposited?

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