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

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.

Express the following linear equations in the form $ax + by + c = 0$ and indicate the values of $a$, $b$ and $c$ in each case : $2 x=-\,5 y$

Given the point $(1,\, 2)$, find the equation of a line on which it lies. How many such equations are there ?

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

$(i)$ $2 x+3 y=4.37$

$(ii)$ $x-4=\sqrt{3} y$

$(iii)$ $4=5 x-3 y$

$(iv)$ $2 x=y$