Question

the taxi fare in a city is as follows: for the first kilometre, the fare is rupee 8 and for the subsequent distance it is rupee 5 per km. taking the distance covered as x km and total fare as rupee y, write a linear equation for this information, and draw its graph

Answer 1

Answer:

The linear equation is Y=5x+8 where x>0

(you can input this into the Desmos graphing calculator to see the graph if you like!)

Step-by-step explanation:

To get the answer is fairly straight forward. If we know that distance covered is x in the equation and we know that a linear equation follows the template Y=mX+b where m is slope and b is the y-intercept. The first step is to fill in what we know. That would look as such Y=_X+_. We can then attempt to fill in the blanks for m and b. Because we know that it is 5 rupees extra per subsequent kilometre we can put 5 as the multiplier for x and there is our m or slope. We now have Y=5x+_. Now for b. B in this case is quite simple as is showing us where the start of the graph is. It is stated that there is a flat fee of 8 rupees, so the total can never be less than 8. Because b is simply where the line intercepts the y axis, and we want it to intercept at 8, we can just put a plus 8. And there you have it Y=5x+8. One important note is that the graph when drawn should be a ray extending from point (0,8). This is because we want to eliminate all of the areas on the plane that would make the fare negative, as we could not have a negative cab fare. This is as simple as plotting the line starting from point (0,8) on the y axis. Happy to help!