 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that find the linear function that relates y to x using the following graph. We know that a linear function is that function whose graph is a straight line and its equation is given by y is equal to m into x plus c, where m represents the slope of a line and c is the y intercept. With this key idea let us proceed to the solution. Now in this question we are given a graph on which points are plotted. The points are with the coordinates minus 1 5.5 b with the coordinates 0,4 c with the coordinates 2,1 and b with the coordinates 4 minus 2. If we join these points we get a straight line. These points lie on a straight line which shows that there is a linear relationship between x and y. Now we shall find that relationship and we know that a straight line has a slope also the intercept made by the line on y axis is given by the point b with the coordinates 0,4. So we say that 4 is the intercept made on y axis that is y intercept is equal to 4. Now we will find slope which is denoted by m and is given by the formula rise upon run let us consider any two points on the line say b and c let us consider points b and c from b we move 3 units down and then move 2 units right to reach point c when we move down it means rise is negative and moving right means run is positive. So we say that slope that is m is given by rise of minus 3 units upon run of 2 units as we have moved 3 units down so we have a rise of minus 3 and 2 units to the right. So we have a run of 2 units. So we have got the value of m mass minus 3 by 2 and we know the y intercept which is denoted by c is equal to 4. From the key idea we know that a linear function is that function whose graph is a straight line and its equation is given by y is equal to m into x plus c where m represents the slope of the line and c is the y intercept. So here the linear relationship is given by y is equal to m into x plus c that is y is equal to m which is equal to minus 3 by 2 into x plus c that is 4. So we have y is equal to minus 3 by 2 into x plus 4 thus we say that y is equal to minus 3 by 2 into x plus 4 is the required equation. This completes our session. Hope you enjoyed this session.