 Hi and welcome to the session. Let's discuss the following question. The question says solve the following inequality graphically in two-dimensional plane. x minus y is less than equal to 2. 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 v 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 satisfy the inequality then the other half plane represents the solution. According to the second rule if the sign of equality is also there with the inequality then the line is included in the solution region and so we draw a dark line and according to the third rule if we have a pure inequality then the points on 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. Let's now begin with the solution given inequality is x minus y is less than equal to 2. Converting this inequality into equation we get x minus y is equal to 2. 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 if y is equal to 0 then x is equal to 2. The two solutions of this equation are 0 minus 2 and 2 is 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 2 is 0. Now the first point is 0 minus 2 this means when fc psi is 0 then ordinate is minus 2 so this is the required point 0 minus 2. Second point is 2 0 this means when ordinate is 0 then fc psi is 2 so this is the required point 2 is 0. Now by the second rule we know that if sign of equality is also there but the inequality then the line is included in the solution region and so we draw a dark line. Now in this question we have x minus y is less than equal to 2. Now the sign of equality is there so this means we will join these two points by a dark line and this line will be included in the solution region so let's now join these two points. This line is representing the equation x minus y is equal to 2. This line divides the plane into two half planes that is 1 and 2. Now we have to identify the half plane represented by an 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 it satisfies the inequality or not. If this point satisfies the 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 that means the half plane which does not contain the point represents the given inequality. 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 less than equal to 2 which is true containing 0 0 represents the inequality x minus y is less than equal to 2. Now let's look at the graph. Now the first half plane contains the point 0 0 and since we have equal to sign in the given inequality so this means this line is also included in the solution region. So the solution region of the given inequality consists of first half plane and this line. Let's now shade this region because the required solution region. So the half plane including the line is the required graphical solution. This is how we find the answer. So this template session I enter.