The graph of the equation $x+y=11$ passes through the first quadrant and .............

Write whether the following statements are True or False? Justify your answers.
$(i)$ The line parallel to the $y$-axis at a distance of $4$ units to the left of the $y$-axis is given by the equation $x = -4$.
$(ii)$ The graph of the equation $y = mx + c$ passes through the origin.

If the temperature of a liquid can be measured in Kelvin units as $x^{\circ} K$ or in Fahrenheit units as $y^{\circ} F$,the relation between the two systems of measurement of temperature is given by the linear equation
$y = \frac{9}{5}(x - 273) + 32$
$(i)$ Find the temperature of the liquid in Fahrenheit if the temperature of the liquid is $313^{\circ} K$.
$(ii)$ If the temperature is $158^{\circ} F$,then find the temperature in Kelvin.

Solve the equation $2y + 1 = y + 4$ and represent the solution$(s)$ on $(1)$ the number line $(2)$ the Cartesian plane.

Solve the equation $3x - 1 = x + 7$ and represent the solution$(s)$ on $(1)$ the number line $(2)$ the Cartesian plane.

The following values of $x$ and $y$ are thought to satisfy a linear equation:

$x$	$1$	$2$
$y$	$1$	$3$

Draw the graph,using the values of $x, y$ as given in the above table.
At what point does the graph of the linear equation:
$(i)$ cut the $x$-axis?
$(ii)$ cut the $y$-axis?