 Hi and welcome to the session. I'm Kanika and I'm going to help you to solve the following question. The question says, give the geometric representations of 2x plus 9 is equal to 0 as an equation. First part is in one variable and second part is in two variables. Let's now start the solution. In the first part we have to give the geometrical representation of 2x plus 9 is equal to 0 in one variable. If this equation is treated as an equation in one variable then it has a unique solution x is equal to minus 9 by 2 which is a point on the number line. So let's now draw the number line. This is the number line. We have marked the positive numbers to the right of the origin and negative numbers to the left of the origin. Now we will mark our required point minus 9 by 2. Now minus 9 by 2 is equal to minus 4.5. So let's now mark minus 4.5. Now this is minus 4.5. So this point is representing the equation 2x plus 9 is equal to 0. So this is the required geometric representation of 2x plus 9 is equal to 0 when it is treated as an equation in one variable. In part we have to give the geometric representation of 2x plus 9 is equal to 0 in two variables. Now the equation 2x plus 9 is equal to 0 can be written as 2x plus 0 into y plus 9 is equal to 0. Right. Now this is the equation in two variables. We know that linear equation in two variables has infinitely many solutions. So this equation will also have infinitely many solutions. And every solution equation is of the form minus 9 by 2 r where is any real number. Let's take the two solutions as x is equal to minus 9 by 2 when y is equal to 0 and x is equal to minus 9 by 2 when y is equal to 2. Now we will plot the solution on the graph. We have drawn the two axes x and y. These two axes are perpendicular to each other. The point of intersection of these two axes is the origin at the origin both x coordinate and y coordinate is 0. Now the two solutions which we have found out is x is equal to minus 9 by 2 when y is equal to 0 and x is also equal to minus 9 by 2 when y is equal to 2. Let's now plot the solution on the graph. Now the first solution is when y is equal to 0 then x is equal to minus 9 by 2. That means x is equal to minus 4.5. This means this is our required point minus 9 by 2 0. Now the second point is when y is equal to 2 then x is equal to minus 9 by 2. So this is our required point minus 9 by 2. Now we will join these two points by a straight line. This is the required line which is representing the equation 2x plus 9 is equal to 0. So this is the required geometric representation of 2x plus 9 is equal to 0 when it is treated as an equation in two variables. So this completes the session. Bye and take care.