Q. The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement.

Q. Express the following linear equations in the form $ax+by+c=0$ and indicate the values of $a,b$ and $c$ in each case:

Q. Which one of the following options is true, and why?
$y=3x+5$ has
(i) a unique solution,
(ii) only two solutions,
(iii) infinitely many solutions

Q. Write four solutions for each of the following equations:
(i) $2x+y=7$
(ii) $\pi x+y=9$
(iii) $x=4y$

Q. Check if $(0,2)$ solution of the equation $x-2y=4$ or not:

Q. Find the value of $k$, if $x=2,y=1$ is a solution of the equation $2x+3y=k$.

Q. Give the equations of two lines passing through $(2,14)$. How many more such lines are there, and why?

Q. From the choices given below, choose the equation whose graphs are given in Fig. (i) and Fig. (ii).

Q. Draw the graph of each of the following linear equations in two variables:
(i) $x+y=4$
(ii) $x-y=2$
(iii) $y=3x$
(iv) $3=2x+y$

Q. 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 many take their contributions as $Rs.x$ and $Rs.y$.) Draw the graph of the same.

Q. 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.

Q. The taxi fare in a city is as follows: For the first kilometre, the fare is $8$ and for the subsequent distance it is $5$ 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.

Q. 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:
$F=\left(\frac{9}{5}\right)C+32$
(i) Draw the graph of the linear equation above using Celsius for $x$-axis and Fahrenheit for $y$-axis.
(ii) If the temperature is ${30}^{o}C$, what is the temperature in Fahrenheit?
(iii) If the temperature is ${95}^{o}F$, what is the temperature in Celsius?
(iv) If the temperature is $0^{o}C$, what is the temperature in Fahrenheit and if the temperature is $0^{o}F$, 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.

Q. If the point $(3,4)$ lies on the graph of the equation $3y=ax+7$, find the value of $a$.

Q. Give the geometric representations of $2x+9=0$ as an equation
(i) in one variable
(ii) in two variable

Q. Give the geometric representations of $y=3$ as an equation
(i) in one variable
(ii) in two variable