 Hi and welcome to the session. In exercise 1 to 8, find the equation of the line which satisfy the given conditions. Fourth one is passing through the point 2, 2 root 3 and inclined with the x axis at an angle of 75 degrees. So, let us start with the solution. An equation of a line passing through the point not y naught, y minus y naught is equal to n times of x minus x naught, where x y is any general point on the line and n is the slope where n is given by tan theta, where theta is the angle made by the line with the x axis. So, here we are given that the point is 2 comma 2 root 3 that is x naught is equal to 2 and y naught is equal to 2 root 3 and inclined with the x axis at an angle of 75 degrees. So, this implies m is equal to tan 75 degrees. Now, let us find the value of tan 75 degrees which is given by tan 45 degrees plus 30 degrees which is further equal to tan 45 degree plus tan 30 degree upon 1 minus tan 45 degree into tan 30 degrees. Now, tan 45 degree is 1 plus tan 30 degrees 1 upon root 3, the denominator we have 1 minus 1 upon root 3. Now, simplifying it we have root 3 plus 1 upon root 3 minus 1, thus m is equal to root 3 plus 1 upon root 3 minus 1 which is the slope of the given line. Now, let us find the equation of the line passing through the point root 3 with slope root over 3 plus 1 upon root over 3 minus 1 is given by y minus 2 root 3 is equal to m that is root 3 plus 1 upon root 3 minus 1 into x minus 2 or this can further be written as y minus 2 root 3 into root 3 minus 1 is equal to root 3 plus 1 into x minus 2 or it can further be written as y into root 3 minus 1 minus 2 root 3 into root 3 is 6 plus root 3 is equal to root 3 plus 1 into x. Now, multiplying this with minus 2 we have minus 2 root 3 minus 2. Now, taking x and y terms on one side we have x into root 3 plus 1 minus y into root 3 minus 1 is equal to minus 6 plus 2 root 3 plus 2 root 3 plus 2 or it further implies root 3 plus 1 into x minus root 3 minus 1 into y is equal to 4 root 3 minus 4 or root 3 plus 1 into x minus root 3 minus 1 into y is equal to 4 times of root 3 minus 1. Hence, the equation of the line is equal to root 3 plus 1 into x minus root 3 minus 1 into y is equal to 4 times of root 3 minus 1. So this is the required equation of the line. This completes the solution. Hope you have understood it. Take care and have a good day.