If $(2,0)$ is a solution of the linear equation $2x + 3y = k,$ then the value of $k$ is

The point of the form $(a, a)$ always lies on:

If $(2,3)$ is a solution of the equation $7x - 3y = a$ and $(a, a+1)$ is a solution of the equation $2x + y = b$,find the values of $a$ and $b$.

The autorickshaw fare in a city is as follows: For the first kilometre,the fare is ₹ $10$,and for the subsequent distance,it is ₹ $3$ per $km$. Taking the distance covered as $x$ $km$ and the total fare as ₹ $y$,write a linear equation for this information and draw its graph. Find the total fare for a journey of $4$ kilometres from the graph.

The work done by a body on application of a constant force is the product of the constant force and the distance travelled by the body in the direction of force. Express this in the form of a linear equation in two variables and draw its graph by taking the constant force as $3$ units. What is the work done when the distance travelled is $2$ units? Verify it by plotting the graph.

Express the following linear equation in the form $ax + by + c = 0$ and indicate the values of $a, b$ and $c$ in each case:
$5x + 3y = 45$