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Draw the graph of each of the following linear equations in two variables:
(i)
(ii)
(iii)
(iv)
(i) 
Observe that x = 0, y = 4 and x = 4, y = 0 are solutions of the above equation. Hence,
| x | 0 | 4 |
| y | 4 | 0 |
The graph for this equation is represented below:
(ii) 
Observe tha x = 4, y = 2 and x = 2, y = 0 are solutions of the above equation.Hence,
| x | 4 | 2 |
| y | 2 | 0 |
The graph for this equation is represented below:
(iii) y = 3x
Observe tha x = −1, y = −3 and x = 1, y = 3 are solutions of the above equation.Hence,
| x | − 1 | 1 |
| y | − 3 | 3 |
The graph for this equation is represented below:
(iv) 3 = 2x + y
Observe tha x = 0, y = 3 and x = 1, y = 1 are solutions of the above equation.Hence,
| x | 0 | 1 |
| y | 3 | 1 |
The graph for this equation is represented below:
Give the equations of two lines passing through (2, 14). How many more such lines
are there, and why?
It can be noticed that point (2, 14) satisfies the equation 7x − y = 0 and x − y + 12 = 0.
Hence, 7x − y = 0 and x − y + 12 = 0 are the two lines passing through the point (2, 14).
It is known that through one point, infinite number of lines can pass through, hence, there are infinite lines passing through the given point.
If the point (3, 4) lies on the graph of the equation, find the value of a.
Putting x = 3 and y = 4 in the given equation,
3y = ax + 7
3 (4) = a (3) + 7
5 = 3a
The taxi fare in a city is as follows: For the first kilometre, the fare is Rs. 8 and for the
subsequent distance it is Rs. 5 per km. Taking the distance covered as x km and total
fare as `Rs. y, write a linear equation for this information, and draw its graph.
Total distance covered = x km
Fare for 1st kilometre = Rs 8
Fare for the rest of the distance = Rs (x − 1) 5
Total fare = Rs [8 + (x − 1) 5]
y = 8 + 5x − 5
y = 5x + 3
5x − y + 3 = 0
It can be observed that point (0, 3) and 
satisfies the above equation. Therefore, these are the solutions of this equation.
| x | 0 | |
| y | 3 | 0 |
The graph of this equation is represented as follows:
It can be noticed that variable x and y are representing the distance covered and the fare paid for that distance respectively. These quantities may not be negative. Hence, only those values of x and y lying in the 1st quadrant will be considered.
From the choices given below, choose the equation whose graphs are given in Fig. (1) and Fig (2)
For figure (1)
Points on the given line are (−1, 1), (0, 0), and (1, −1).
It can be observed that the coordinates of the points of the graph satisfy the equation x + y = 0. Therefore, x + y = 0 is the equation corresponding to the graph.
Hence, (ii) is the correct answer.
For figure (2)
Points on the given line are (−1, 3), (0, 2), and (2, 0). It can be observed that the coordinates of the points of the graph satisfy the equation y = − x + 2.
Therefore, y = − x + 2 is the equation corresponding to the graph shown in the second figure.
Hence, (iii) is the correct answer.
If the work done by a body on application of a constant force is directly proportional
to the distance travelled by the body, express this in the form of an equation in two
variables and draw the graph of the same by taking the constant force as 5 units. Also
read from the graph the work done when the distance travelled by the body is
(i) 2 units
(ii) 0 unit
Let the distance travelled and the work done by the body be x and y respectively.
Work done ∝ distance travelled
y ∝ x
y = kx
Where, k is a constant
If constant force is 5 units, then work done y = 5x
It can be observed that point (1, 5) and (−1, −5) satisfy the above equation. Therefore, these are the solutions of this equation. The graph of this equation is constructed as follows.
(i)From the graphs, it can be noticed that the value of y corresponding to x = 2 is 10. This implies that the work done by the body is 10 units when the distance travelled by it is 2 units.
(ii) From the graphs, it can be noticed that the value of y corresponding to x = 0 is 0. This implies that the work done by the body is 0 units when the distance travelled by it is 0 unit.
Yamini and Fatima, two students of Class IX of a school, together contributed Rs. 100
towards the Prime Minister’s Relief Fund to help the earthquake victims. Write a linear
equation which satisfies this data. (You may take their contributions as Rs. x and
Rs. y.) Draw the graph of the same.
Let the amount that Yamini and Fatima contributed be x and y respectively towards the Prime Minister’s Relief fund.
Amount contributed by Yamini + Amount contributed by Fatima = 100
x + y = 100
It can be observed that (100, 0) and (0, 100) satisfy the above equation. Therefore, these are the solutions of the above equation. The graph is constructed as follows.
Here, it can be seen that variable x and y are representing the amount contributed by Yamini and Fatima respectively and these quantities cannot be negative. Hence, only those values of x and y which are lying in the 1st quadrant will be considered.
In countries like USA and Canada, temperature is measured in Fahrenheit, whereas in
countries like India, it is measured in Celsius. Here is a linear equation that converts
Fahrenheit to Celsius:
(i) Draw the graph of the linear equation above using Celsius for x-axis and Fahrenheit
for y-axis.
(ii) If the temperature is 30°C, what is the temperature in Fahrenheit?
(iii) If the temperature is 95°F, what is the temperature in Celsius?
(iv) If the temperature is 0°C, what is the temperature in Fahrenheit and if the
temperature is 0°F, what is the temperature in Celsius?
(v) Is there a temperature which is numerically the same in both Fahrenheit and
Celsius? If yes, find it.
(i) 
It can be observed that points (0, 32) and (−40, −40) satisfy the given equation. Therefore, these points are the solutions of this equation.
The graph of the above equation is constructed as follows.
(ii) Temperature = 30°C
Therefore, the temperature in Fahrenheit is 86°F.
(iii) Temperature = 95°F
Therefore, the temperature in Celsius is 35°C.
(iv)
If C = 0°C, then
Therefore, if C = 0°C, then F = 32°F
If F = 0°F, then
Therefore, if F = 0°F, then C = −17.8°C
(v)
Here, F = C
Yes, there is a temperature, −40°, which is numerically the same in both Fahrenheit and Celsius.
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