 Hi and welcome to the session let's discuss the following question. The question says the taxi fare in a city is as follows for the first kilometer the fare is rupees 8 and for the subsequent distance it is rupees 5 per kilometer taking the distance covered as x kilometer and the total fare as rupees y write a linear equation for this information and draw its graph let's now start the solution total distance covered is x kilometer now in x kilometer first kilometer is covered at rupees 8 the subsequent distance that means x minus 1 kilometer is covered at rupees 5 per kilometer so for the first kilometer rupees 8 the subsequent distance minus 1 into 5 is y now this means fare for the first kilometer plus fare for the subsequent distance is equal to rupees y minus 1 into 5 is equal to y and this implies 8 plus 5x minus 5 is equal to y and this implies 5x plus 3 is equal to y and this implies 5x minus 5 plus 3 is equal to 0 this is the required linear equation now we have to draw the graph of this equation so for drawing the graph we need at least two solutions of this equation so let's now find the two solutions of this equation when x is equal to 0 then the given equation reduces to 5 into 0 minus 5 plus 3 is equal to 0 and this implies minus 5 plus 3 is equal to 0 and this implies y is equal to 3 and when y is equal to 0 then the given equation reduces to 5x minus 0 plus 3 is equal to 0 and this implies 5x plus 3 is equal to 0 and this implies x is equal to minus 3 by 5 let's now represent the solution in the tabular form so let's make a table when x is equal to 0 then y is equal to 3 and when y is equal to 0 then x is equal to minus 3 by 5 let's now plot this point on the graph we have drawn the two x's x and y these two axes are perpendicular to each other the point of intersection of these two axes is the origin at the origin both the x coordinate and y coordinate is 0 and we know that x coordinate is also known as abscissa and y coordinate is also known as ordinate now these are the two solutions which we have found out so let's now plot these points on the graph now the first point is 0 3 this means when abscissa is 0 then ordinate is 3 so this is the required point 0 3 now the next point is minus 3 by 5 0 this means when ordinate is 0 then abscissa is minus 3 by 5 that means minus 0.6 so this is the point minus 3 by 5 0 now we will join these two points by a straight line this is the line which is representing the equation 5x minus 5 plus 3 is equal to 0 so this completes the session by and take care