 Hello and welcome to this session. In this session we will discuss a question which says that the category shows the number of entrants in America for certain years since 1982. Then, draw the scatter diagram and determine the relationship. Also draw the line of fit and find the equation of this line of best fit. Create the number of entrants in the year 1994. Now let us start with the solution of the given question. Now here, we have given a table showing the number of entrants since the year 1982. Here, years are written in numbers. The first is three. That means for three years since 1982, first of all we have to make a scatter diagram for this data. So here, let us take number of years since 1982 on x-axis and number of entrants on y-axis choosing an appropriate scale, a scale of 500 on y-axis and a scale of 2 on x-axis. And now we will plot all these ordered pairs on the graph. Like the first ordered pair here is three, 2700 that is, is three and y-coordinate is 2700 and the corresponding point 200 on y-axis we get which represents the ordered pair three 2700. And similarly, we will plot the other order. So we have plotted all the ordered pairs on the graph, scatter diagram for the given data. Now here, we can see that there exists now here with increase in number of years since 1982. The number of entrants has also increased. Now let us draw the line of fit. Now there is no line that passes through all the data points. So we draw a line that passes close to the maximum at the line of best fit. Now next, we have to find the equation of the line of best fit. Now we know that equation of line in slope intercept form is y is equal to mx plus b where m is the slope and v is the y-intercept of this line. And let us find the slope m of the given line. Yes, we will take any two points that lie on this line and these points may or may not be given in the data. Now here we can see that these two points lie on this line. Now coordinates of this point are 3700 and coordinates 11800. Now slope is equal in y upon change slope m is equal to 800 minus 2700 whole upon change in x that is 11 minus 3 isn't 100 upon which is equal to 262.5. Now let us find the y-intercept v. For this, we will take any point that lies on this line. Let us take this point with coordinates. This point is 3 and y coordinate of this point is 2700. Select this v equation number 1. Supporting x is equal to 3 and y is 100 in equation 1. v that is equal to into x is 3 v. 7700 is equal to 787.5 plus b which implies v is equal to 2700 minus 787.5 912. So we have obtained the values of m's values in equation 1. Requires the line is y is equal to 1,912. We also require equation of the line of best friend. Now we have to estimate the number of entrants in the year 1994. Number of 1982 so here number of is 1982 to 1994 is equal to 1994 minus 1982 which is equal to the number of entrants. We have to find the corresponding value of y. Now let this be equation number 2. In equation 2 we get y is equal to 1,912.5 equal to 3,112. Number of entrants cannot be in decimals so y is equal to hence number of entrants in the year 1962. So this is the solution of the given question and that's all for this session. Hope you all have enjoyed this session.