 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that Mike is working in a restaurant as a waiter. He has an extra income of tips which he gets from the customers whom he had attended. He decides to note down his earnings from tips. He noted that for working 3 hours he earns $38.4 for 5 hours he earns $64 and for 6 hours he earns $76.8 Represent the information graphically and explain what does this layer of line represents. We know that we can conclude a proportional relationship from graph if there is constant rate of change of values of x and y between any two points on graph also whenever a line passes through a region that is 00 and then limit rate of slope is given by changing y that is y-0 by changing x that is x-0 and is equal to y upon x with this key idea we proceed to the solution. Now in this question we are given that Mike is working in a restaurant as a waiter. He noted that for working 3 hours he earns $38.4 for 5 hours he earns $64 and for 6 hours he earns $76.8. Let us make the table as given information. So here we have for 3 hours night earns $38.4 for 5 hours he earns $64 and for 6 hours he earns $76.8. Now let us see each ratio that is earnings upon number of hours and we get earnings that is $38.4 by 3 which is equal to $12.8 and then $64 by 5 and then again equal to $12.8 and then we have $76.8 by 6 which is equal to $12.8. So we have d upon h is equal to $12.8 where d is the earnings in dollars and h is the number of hours and thus we get d is equal to $12.8 into h since each ratio is same. So the two quantities are proportional. As we know from the key idea that we can conclude a proportional relationship from graph f where f constant rate of change of values of x and y between any two points on graph. Also we know that it is a linear relationship. So the graph will be a straight line passing through the origin that is 00 and now we shall make its graph. Now take number of hours along horizontal axis and earnings in dollars along vertical axis and we shall plot these points 1 by 1 on the graph. First we shall take 3 38.4. Here we take 3 along horizontal axis and 38.4 along vertical axis and we get the point 3 38.4. Now we shall plot the point 5 64. For this we move 5 along horizontal axis and 64 along vertical axis and we get the point 5 64. And lastly we shall plot the point 6 76.8 and here we get the point 6 76.8 and by joining all these points we get a straight line and we see that this line passes through the origin that is 00. And from the key idea we know that we can conclude a proportional relationship from graph f a line passes through the origin that is 00 and then the unit rate or slope will be equal to y by x. So we know that in a proportional relationship slope is equal to y upon x from this graph we take the value of y as 38.4 and the value of x as 3 and therefore we get y by x is equal to 38.4 by 3 and is equal to 12.8 which is also called as unit rate. It means for working 1 hour like earns $12.8 from tips so we can say like earns $12.8 per hour from tips which is the required answer. This completes our session. Hope you enjoyed this session.