 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 a following inequality graphically in two-dimensional plane. 3x plus 4y is less than or equal to 12. 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 should 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 AB not on the line. Generally, we take this point as 0, 0. 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. If it does not satisfy 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. So we draw a dark line. And according to the last rule, if we have a pure inequality, then the points of the corresponding line are not to be included in the solution region. So we draw a dotted line. With the help of these three rules, we will solve the question so always remember these rules. Let's now begin with the solution. Now, the given inequality is 3x plus 4y is less than equal to 12. Now, the corresponding equation is x plus 4y is equal to 12. Now, we will plot a 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. When x is equal to 0, then y is equal to 3. And when y is equal to 0, then x is equal to 4. So the two solutions of this equation are 0, 3, and 4, 0. Now, we will plot these two points on the graph. So let's make a graph now. Points which we have to plot is 0, 3, and 4, 0. Now, the first point is 0, 3. This means when epsilon is 0, then ordinate as 3. So this is the required point 0, 3. And the second point is 4, 0. This means when ordinate is 0, then abscissa is 4. So this is the point 4, 0. Now, according to the second rule, we know that if 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 in the solution region. Now, in the given question, we have 3x plus 4y is less than equal to 12. Now, the sign of equality is there. So this means that we will join these two points by a dark line. And this line will be included in the solution region. So now, join these two points. This is the line which is representing the equation 3x plus 4y is equal to 12. This line divides this plane in two half planes, that is 1 and 2. Now, according to the first rule, for identifying the half plane represented by an inequality, we have to first take any point AB, 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. If it does not satisfy the inequality, then the other half plane represents the solution. Now, substitute this point in the given inequality, that is 3x plus 4y is less than equal to 12. Now, by substituting x and 0 and y as 0, we get 0 less than equal to 12, which is true. Hence, the plane 2, 0 represents the inequality. At the graph, first half plane contains the point 0, 0. So the solution region of the given inequality consists of first half plane and this line. Let's now shape this region. The shaded half plane, the line, is the required graphical solution. This is our required answer. Bye and thank you. Hope you have enjoyed the session.