Question

If the relationship between the total cost ‘y’ of buying the materials and renting the tools at Store C and the number of days ‘x’ for which the tools are rented is graphed in the xy-plane, what does the slope of the line represent?
(a) The total cost of the project.
(b) The total cost of the materials.
(c) The total daily cost of the project.
(d) The total daily rental costs of the tools.

Answer 1

Hint: We start solving the problem by writing the function for the total cost ‘y’ by assuming the variables for the cost for buying the materials and cost of renting the tools. We then find the function for the total rental cost using the number of days as rental cost on tools is imposed based on the number of days. We then substitute this function in the total cost and compare with the equation of the straight line to get the slope of the line.

Complete step-by-step answer:
According to the problem, we are given that the relation between the total cost ‘y’ of buying the materials and renting the tools at Store C and the number of days ‘x’ for which the tools are rented is graphed in the xy-plane. We need to find what the slope of that line represents.
Let us first find the function ‘y’. We can see that the total cost is the sum of cost for buying the materials and cost of renting the tools. Let us assume the cost for buying the materials and cost of renting the tools as ‘b’ and ‘a’ respectively.
So, we get \[y=b+a\] ---(1).
According to the problem we are given that the cost of renting the tools will be varied with the number of days ‘x’.
So, let us assume the renting cost as $c=mx$ ---(2), where m is the cost for renting a tool in a single day.
Let us substitute equation (2) in equation (1).
So, we get \[y=mx+a\]. On comparing this with the standard equation of straight line $y=mx+c$, we get ‘m’ as the slope of the line which is the daily rental cost of the tools.
The correct option for the given problem is (d).

So, the correct answer is “Option (d)”.

Note: Whenever we get this type of problem, we first try to find the functions for the quantities given in the problem. We should understand what is variable (the cost which is dependent on the total no. of days) and fixed cost (the cost which is independent on the total no. of days) while solving this problem. We should know that the total cost function need not be the straight line always and we need to derive the function according to the problem.