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

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

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.

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 $30\,^oC$,what is the temperature in Fahrenheit?
$(iii)$ If the temperature is $95\,^oF$,what is the temperature in Celsius?
$(iv)$ If the temperature is $0\,^oC$,what is the temperature in Fahrenheit and if the temperature is $0\,^oF$,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.

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

For each of the graphs given in the figure,select the equation whose graph it is from the choices given below:
$(a)$ For Fig. $(i)$,
$(i)$ $x+y=0$ (ii) $y=2x$ (iii) $y=x$ (iv) $y=2x+1$
$(b)$ For Fig. (ii),
$(i)$ $x+y=0$ (ii) $y=2x$ (iii) $y=2x+4$ (iv) $y=x-4$
$(c)$ For Fig. (iii),
$(i)$ $x+y=0$ (ii) $y=2x$ (iii) $y=2x+1$ (iv) $y=2x-4$