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?

hintHint:

First we find the total cost of the tent for every hour and make a table with x as the number of hours rented and y as the total cost of the tent. We use this data to plot a graph for the relationship.
The equation of line in slope- intercept form is y = mx + c, where m is slope and c is the y- intercept. We find m and c from the data in the table to get the required equation.

The correct answer is: y = 500x + 100


    Step by step solution:
    The cost of tent per hour = Rs.500
    Set up fee = Rs.100
    For the first hour, the total cost = Rs.(100 + 500) = Rs.600
    In the second hour, the set up fee is still Rs.100, and the cost of tent = Rs(500*2) = Rs.1000
    The total cost for 2 hours = Rs.(1000 + 100)= Rs.1100
    Continuing this way,
    The total cost for 3 hours = Rs.(500 × 3 + 100) = Rs.1600
    The total cost for 4 hours = Rs.(500 × 4 + 100) = Rs.2100
    The total cost for 4 hours = Rs.(500 × 5 + 100) = Rs.2600
    Now, 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 graph


    The 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 open parentheses straight x subscript 1 comma straight y subscript 1 close parentheses and open parentheses straight x subscript 2 comma straight y subscript 2 close parentheses satisfying the equation, the slope is given by
    straight m equals fraction numerator straight y subscript 2 minus straight y subscript 1 over denominator straight x subscript 2 minus straight x subscript 1 end fraction
    Taking any two points from the table and denoting them as

    open parentheses straight x subscript 1 comma straight y subscript 1 close parentheses equals left parenthesis 1 comma 600 right parenthesis text  and  end text open parentheses straight x subscript 2 comma straight y subscript 2 close parentheses equals left parenthesis 2 comma 1100 right parenthesis, we have

    m = fraction numerator 1100 space minus space 600 over denominator 2 space minus space 1 end fraction

    m = 500 over 1 = 500
    Next, for finding the y-intercept, we input any value from the table in the equation y = mx + c
    We choose the first point (1,600), and using it in the above equation, we have

    600 = m × 1 + c
    Putting the value of m in the above relation, we have

    600 = 500 × 1 + c
    Simplifying, we have

    600 = 500 + c
    Thus, we get

    c = 600 - 500 = 100
    So, 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.

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