 Hello and welcome to the session. In this session, we will discuss a question which says that use the best fit line that shows average and maximum longevity of animals in productivity and then write the equation in slope intersect form for the best fit line and second thought is use the equation to predict the maximum longevity of animals for average longevity of 47 years. Now let us start with the solution of the given question. Now in this second thought, we are given relationship between average and maximum longevity of animals. Now here as this line is moving upwards, so there is a positive linear relationship between average and maximum longevity of animals. Here with increase in average longevity, the maximum longevity also increases and now we will find equation of best fit line in slope intersect form. Now equation of line in slope intersect form is y is equal to mx plus b. Now we will take any two points which lie on this line. Now here this is the first point and let this be the second point and coordinates of this point are 15, 40 and coordinates of this point are 35, 70. So slope at this line will be equal to change in y upon change in x. Slope m is equal to change in y that is 70 minus 40 whole upon change in x that is 35 minus 15 which is equal to 30 upon 20 which is equal to 3 upon 2 and this is equal to 1.5 and now we will find the y intersect b. For this we will take any point which lies on this line. Now let this equation be equation 1. So put in 15 and y is equal to 40 in equation 1 we get t is equal to now here slope m is equal to 3 upon 2 so this is equal to mx that is 3 upon 2 into 15 b. 1.5 into 15 plus b and this implies 40 is equal to 22.5 plus b and this gives b is equal to 30 minus 22.5 which is equal to 17.5 equal to 1.5 and b is equal to 17.5 so required equation of best fit line is y is equal to mx that is 1.5 into x y equation of the best fit line. Now in the second part we have to use this equation to predict the maximum longevity of animals for every longevity of 37 years it means in the second 37 the corresponding value of y. Now let this be equation number 2 so put in 2 to 47 in equation 2 we get x 17.5 which is equal to 17.5 equal to 88 which is half the given question hope you all have enjoyed the session.