 Hi and welcome to the session. I'm Kanika and I'm going to help you to solve the following question. The question says solve the following inequality graphically in two dimensional plane. 2x-3y is greater than 6. Before solving this question we should know that a line divides the Cartesian plane into two half planes and the graph of inequality will be one of the half planes and we shall show the solution by shading in the corresponding half plane. We shall follow the following rules to identify the half plane represented by an inequality. According to the first rule we have to take any point a b not on the line and then we have to check whether it satisfies the inequality or not. If the point satisfies the inequality then the inequality represents that particular half plane containing the point but if the point does not satisfies the inequality then the other half plane represents the solution. According to the second rule if sign of equality is also there with the inequality then the line is included in the solution region and so we draw a doubt line in the solution region and according to the third rule if we have a pure inequality then the points of the corresponding line are not to be included in the solution region and so we draw a dotted line. With the help of these three rules we will solve this question so always remember these rules. Now begin with the solution. Given inequality is 2x-3y is greater than 6. Now converting this inequality into equation we get 2x-3y is equal to 6. Now we have to plot the graph of this equation for plotting the graph we need at least two solutions of this equation. So let's first find the two solutions of this equation. If x is equal to 0 then y is equal to minus 2 and f y is equal to 0 then x is equal to 3. So the two solutions of this equation are 0 minus 2 and 3 0. Now we will plot these two points on the graph. So let's make a graph now. The two points which we have to plot are 0 minus 2 and 3 0. Now the first point is 0 minus 2 this means when fcca is 0 then ordinate as minus 2. So this is the required point 0 minus 2 and the second point is 3 0 this means when ordinate is 0 then fcca is 3. So this is the required point 3 0. According to the third rule we know that if we have a pure inequality then the points of the corresponding lines are not included in the solution region and so we draw a dotted line. Now in this question we have 2x minus 3y is greater than 6. We have a strict inequality there that means we will join these two points by a dotted line and this line will not be included in the solution region. So let's now join these two points by a dotted line. This line is representing the equation 2x minus 3y is equal to 6 and this lines divides the plane into two half planes that is 1 and 2. Now we have to identify the half plane represented by then given inequality. According to the first rule we have to select a point which does not lie on the line and then we have to check whether this point satisfies the given inequality or not. If this point satisfies the given inequality then the inequality represents that particular half plane containing the point but if the point does not satisfy the inequality then the other half plane represents the solution. Now in this question as the point 0 0 does not lie on this line so we can take the point as 0 0. Now substitute x as 0 and y as 0 in the given inequality by substituting we get 0 greater than 6 which is not true. Hence the half plane not containing 0 0 represents the inequality x minus 3y greater than 6 and is the solution region. Now let's look at the graph. Now the second half plane does not contain the point 0 0 and as we have strict inequality so this means this line will not be included in the solution region. So this means the solution region of the given inequality consists of second half plane excluding this line. So let's now shade this region. This is the required solution region. So the shaded half plane excluding the line is the required graphical solution. So this is our required answer. So this can be exercised by indeed kill.