Maths-
General
Easy

Question

Gopi wants to rent a tent for an outdoor celebration. The Cost of tent is Rs.500 per hour, plus an additional Rs.100 set-up fee. a) Draw a graph to show the relationship between the number of hours the tent is rented, x, and The total cost of the tent Y.b) What is the equation of the line in slope- intercept form?

Hint:

The correct answer is: y = 500x + 100

Step by step solution:The cost of tent per hour = Rs.500Set up fee = Rs.100For the first hour, the total cost = Rs.(100 + 500) = Rs.600In the second hour, the set up fee is still Rs.100, and the cost of tent = Rs(500*2) = Rs.1000The total cost for 2 hours = Rs.(1000 + 100)= Rs.1100Continuing this way,The total cost for 3 hours = Rs.(500 × 3 + 100) = Rs.1600The total cost for 4 hours = Rs.(500 × 4 + 100) = Rs.2100The total cost for 4 hours = Rs.(500 × 5 + 100) = Rs.2600Now, taking time (in hours) to be in x-axis and the total cost (in Rs.) to be y- axis, we draw the following table.Now, we plot these points on the graphThe line intercept form of a line is y = mx + c, where  is the slope of the line and  is the y-intercept of the line.First, we find the slope of the equation.For two points  and  satisfying the equation, the slope is given byTaking any two points from the table and denoting them as, we havem = m =  = 500Next, for finding the y-intercept, we input any value from the table in the equation y = mx + cWe choose the first point (1,600), and using it in the above equation, we have600 = m × 1 + cPutting the value of m in the above relation, we have600 = 500 × 1 + cSimplifying, we have600 = 500 + cThus, we getc = 600 - 500 = 100So, the y-intercept c = 100,Using the value of m and c, we get the required equation,y = 500x + 100

Instead of using these particular points to find the slope and the y-intercept, we can use any other points from the table; we will get the same equation at the end. We can also verify this equation by inserting the points from the table and checking if the equation is satisfied. Finally, we can find the line in any other forms of a straight line.