 Hello and welcome to the session. In this session we will discuss a question which says that the cost of renting a car for one day is $52 plus $0.25 per mile. Let m represents the number of miles the car was driven and let c represents the rental cost in dollars for a day. When in the first part, write an equation for the rental cost of the car in terms of number of miles driven. In the second part, complete the following table of values. Also explain the meaning of values found in the table. And in the third part, find the initial value of cost and rate of change. Now let us start with the solution of the given question. Now here we are given that the cost of renting a car for one day is $52 plus $0.25 represents the number of miles the car was driven and c represents the rental cost in dollars for a day. Now in the first part, we have to write an equation for the rental cost of the car in terms of number of miles driven. Now the cost of renting a car for one day is $52 plus $0.25 per mile, c represents rental cost and m represents the number of miles driven. The cost of rent will be equal to 0.25 into m plus rental charge is represented by c and this is equal to 0.25 m plus rental charge which is $52. We got the equation as c is equal to 0.25 m plus. So this is the required equation for the rental cost of the car in terms of number of miles driven. Now in the second part, we have to complete this table of values. We have to explain the meaning of values found in the table. Now here we have to complete this table. Number of miles driven are given as $54 and for this we have to find the rental cost c. Now we have obtained an equation for the rental cost of the car in terms of number of miles driven equation number one. So putting equation one we get $25 into $54. This implies c is equal to, now $0.25 into $54 is $13.5 and this gives c is equal to, we get c is equal to $65.5. When car was driven $65. We have to find the value of m. c is equal to $72. In equation one we get $72 is equal to $0.25 into m and this implies $72 minus $52 is equal to $0.25 into m which gives is equal to $0.25 into m and this implies m is equal to $20 upon $0.25 which is equal to $20 into $100 upon $25 and this is equal to, now $25 into $4 is $100 and $4 into $20 is, c is equal to $72 m is equal to, so this the rental cost the car was driven. In the third part we have to find the initial value. Now we know that equation of the line is of the form y is equal to mx plus b. There y is the dependent variable, x is the independent variable, the slope b represents also, b represents the initial value. Now here we have this equation where the rental cost c in terms of number of miles equation is of the form y is equal to mx plus b where c is the dependent variable, is the independent variable. Now we know that coefficient of the independent variable represents the rate of change, so here the rate of change is equal to $0.25, here y intersect is $52 which means the initial value is equal to $52. It can be obtained by putting m is equal to 0. In this equation this means even if we do not drive the car then also we have to pay the rent of the car for a day that is $52 thus initial charges $2. Initial value of cost $2 and rate of change is $0.25. That is all for this session. Hope you all have enjoyed this session.