 Hello and welcome to the session. In this session we will discuss a question which says that draw a graph of proportional relationship for the following statement. And the statement is, Davis adds three dollars to his savings account each week. Also write the constant of proportionality. Now before starting the solution of this question, you should know a result. Now by constant of proportionality, we mean that the ratio between two quantities is always same. For example, two quantities y and n, y upon x is equal to k where k is a constant, then k is called the constant of proportionality. And this relationship can also be written as y is equal to kx and we say that y is directly proportional to x. Now this result will work out as a key idea. First we are looking at the given question. Now let us start with the solution of the given question. First question, we are given that Davis adds three dollars to his savings account each week. It means if Davis has in the first week, then in the second week, he will add three dollars more. It means he has the total of six dollars in the second, then again he will add three dollars to his account and in the third week, the total will become six is equal to then for the fourth week, he will have nine dollars plus three dollars, that is twelve dollars and so on. Now let us draw a table. Now for these observations, we have drawn a table and in the first row, we will write the weeks and in the second row, we will write the dollars. That is for the first week, we have three dollars, then for the second week, we have six dollars, for the third week, we have nine dollars, then for the fourth week, we have twelve dollars. Now from the table, the ratio of dollar is to week. Now here you can see the ratio is three is to one or you can write it as three by one, which is equal to three. Then here in the second observation, we have six dollars in the second week, so the ratio will be by two, which is equal to three. Then for the third week, it is nine by three, which is again three and then for the fourth week, the ratio will be twelve by four, which is equal to three. Now we have three by one is equal to six by two is equal to nine by three is equal to twelve by four and all of them are equal to three. It means all these ratios are in proportion and from the key idea, we know that for the two quantities y and x, if y upon x is equal to k, so here in this case, we have k as the constant of proportionality. So here as we have three by one is equal to three, six by two is equal to three, nine by three is equal to three and twelve by four is equal to three. So three is the constant of proportionality, thus Davis per week. Now in the question, we have to draw a graph of the proportional relationship for this statement. Now for the graph, coordinate v the week and while coordinate v the dollars. Now we can see that we are getting the ratio of dollars is to be equal to three. So we have y component that is y, which is the dollars over the x coordinate that is v is equal to three. The ratio of dollars and week, which means y upon x is equal to three. Now from the key idea, if y upon x is equal to k, then we can write this relationship as y is equal to kx. So this implies y is equal to, now we will draw the graph for this equation. Now for x is equal to zero, we have y is equal to three into zero, which is equal to zero. Which means it passes through the origin as the coordinates of the region are zero to zero. Now we will draw the points which are mentioned in this table on the graph. And where we know that x coordinate is the week and y coordinate is the dollar. The point zero to zero that is the origin on the graph. So this is the origin that is the point zero to zero. The next point which we will plot on the graph is one point whose coordinates are one. Now the next point which we will plot on the graph is two point whose coordinates are two. We will plot the points three, nine. We have plotted all the points on the graph. Now by joining all these points, we will get a straight line which is passing through the origin. Now this straight line describes the proportional relationship which is y, that y is directly proportional to x of three is the constant of proportionality. So this is the solution of the given question. And that's all for this session. Hope you all have enjoyed the session.