 Hello and welcome to the session. In this session we will use the equation of line of best fit to make predictions. And we will learn to write the equation of line of best fit for the linear relationship with the help of scatter diagram. We will see how we can determine the values from the equation. We will make use of slope and intersect to form the linear equation. We know that any linear equation is of slope intersect form that is y is equal to mx plus b where m is the slope and b is the y-intercept. And we also know that slope m is equal to change in y upon change in x which means m is equal to difference in y coordinates upon difference in y coordinates h and b is the point where the line meets the y-exit. It is given by the habit pair 0b that is the point where x coordinate is 0 and y coordinate is b. Now when we draw line of best fit it is a straight line which is drawn so that all the points are close to the line on either side. The line may also pass. So we will follow the given steps to write the equation of the line of best fit for a linear relationship. In the first step we will draw a scatter diagram and then we will draw a straight line that is the line of best fit paying attention to the closeness of all other points. And in the next step we will find the slope m for this line. For this we will take every two points this point which coordinates x1, y1, point which coordinates x2, y2 and both these points should lie on this line. And these three points may or may not be the original data points and then slope m will be equal to change in y that is y2-y1 upon change in x that is x2-y1. In the next step we will find the y-intercept b and we know that where the line meets the y-axis here this is the point where this line of best fit meets the y-axis of this point will be 0b and from this point we will get the value of b. Then in the next step y is equal to mx plus b that equation of this best fit and then we can determine or predict the values of value. Now let us discuss it with the help of an example. Where it is given means that scores and their number are. Now for this data we have to make a scatter plot and then we have to draw a line of best fit and then from this line of best fit we have to approximate the linear equation that models the given data acts as a student with fill. Now first of all let us make a scatter plot for this given data. For this let us take a score on yx choosing an appropriate scale on the graph like first pair that is the first of 65 represents the object pair we can plot all the other object pairs also. So we have constructed the line of best fit paying attention to the closeness of all points. So we have drawn the line of best fit through some points. Now here you can see that this line is moving downwards so it is a linear negative relationship. As the number of x's increases the marks scored decreases. Now let us find the slope of this line. For this we will take any two points lying on this line. Now let these points be 1.880 and 920. Now these points on the line are not given in the data. So the points we take on line may or may not be given in the data. We can make using the points. Now slope m is equal to on change in x that is 9 minus 1 point minus 60 upon minus 60 upon 72 into 10 which is equal to minus 25 upon 3. So slope is equal to minus 25 upon 3. Now let us find the y intercept v in graph. But line passes only through one point that is so line cuts the y axis at this point v is equal to 95. The required equation of best fit line is y is equal to mx. Now m here is minus 25 upon 3. So y is equal to minus 25 upon 3 into x plus v which is 95. Required equation is y is equal to minus 25 upon 3 into x plus 95. Now also we have to determine how many marks we are student with four accents expect. It means for x is equal to 4 we have to find value of y. Now like this the equation number 1. Now putting x is equal to 4 in 1 we get y is equal to minus 25 upon 3 into 4 plus 95. And this implies y is equal to minus 100 upon 3 plus 95. Now this is equal to minus 100 plus 285 upon 3 which is equal to 18 upon 3 which is equal to approximately. Can expect approximately. Now let us see another method of finding intercept. Now we have already obtained slope is equal to minus 25 upon 3. And we know that equation of a line in slope intercept form is y is equal to mx plus v. Now take any point on the line let it be the point. Now like this p equation number 2. So putting x is equal to 9 y is equal to 20 into we get minus 25 upon 3 into 9 plus v which implies 20 is equal to minus 75 plus v which further gives v is equal to 75 plus 20 which is equal to 95. So by this method also we obtain y intercept is equal to 95. So the required equation of best fit line is y is equal to which is minus 25 upon 3 into x plus v which is 95. So from this method also we can obtain equation of best fit line. So in this session we have learnt to write the equation of best fit line for the linear relationship with the help of scatter diagram. And this completes our session hope you all have enjoyed the session.