 Hello and welcome to the session. I am Asha and I am going to help you with the following question that says, find equation of the line passing through the point two two and cutting off intercepts on the axis whose sum is nine. So let's begin with the solution, the intercept form of a line upon A plus Y upon B is equal to one. Now here we are given that the line is cutting off intercepts on the axis whose sum is nine. So we are given that A plus B is equal to nine. Let this be equation number one. Now the line passes through the point two two therefore on substituting the values of X and Y in the intercept form of the line we have two upon A plus two upon B is equal to one or we have two B plus two A is equal to AB. So this is the sign equation. Now we will solve equation one and two to get the values of A and B. Now from equation one and two have two can be written as taking two common from the left hand side here A plus B is equal to AB and A plus B is equal to nine. So we have two into nine is equal to AB. So this implies AB is equal to 18. And also A plus B is equal to nine. So substituting the value of A which is 18 upon B in this equation it can further be written as 18 upon B plus B is equal to nine or we have B square minus nine P plus 18 is equal to zero. Now splitting the middle term it can be written as B square minus six P minus three B plus 18 is equal to zero. Now taking B common from the first two terms and minus three common from the last two terms it can further be written as B into B minus six minus three times of B minus six is equal to zero or we have B minus six into B minus three is equal to zero. Now as we know if the product of two numbers is equal to zero then at least one of them is zero. So this implies either B minus six is equal to zero or B is equal to three. So this implies B is equal to six or three. And substituting the values of B that is six and three in this equation we will get the values of A three or six. So this implies if B is equal to six then A is equal to three and if B is equal to three then A is equal to six. Now intercept form upon A plus Y upon B is equal to one. So first let us consider the case when A is equal to three and B is equal to six. So we have X upon three plus Y upon six is equal to one or we have taking this x-axis we have two X plus Y is equal to one or two X plus Y is equal to six. So this is the first equation and now let us consider A to be six and B is equal to three. An equation of the line is X upon six plus Y upon three is equal to one or we have six LCM X plus two Y is equal to one or we have X plus two Y is equal to six. So this is the second equation of the line and thus our answer is the equation of the lines are two X plus Y minus six is equal to zero and X plus two Y minus six is equal to zero. So this completes the session take care and have a good day.