Draw the graph of the linear equation whose solutions are represented by the points having the sum of the coordinates as $10$ units.

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

The force exerted to pull a cart is directly proportional to the acceleration produced in the body. Express the statement as a linear equation of two variables and draw the graph of the same by taking the constant mass equal to $6 \,kg$. Read from the graph,the force required when the acceleration produced is $(i)$ $5 \,m/s^2$,$(ii)$ $6 \,m/s^2$.

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

Draw the graphs of linear equations $y=x$ and $y=-x$ on the same Cartesian plane.
What do you observe?