 Hello and welcome to the session. In this session, we will discuss the question which says that Samantha has shared postcards in her postcard collection. She decides that from now on every time she goes out on vacation, she will buy 6 postcards to add to her collection, write an equation to represent the number of postcards she will have after x number of vacations, write the equation, find the rate of change and initial value. Now before starting the solution of this question, we should know a result. Now every linear equation is of the form y is equal to mx plus b and the resultant and equation of line in slope intercept form where m represents slope and b represents y intercept of the line. Now this result will welcome to us the key idea for solving a given question. Now let us start with the solution of the given question. The way we are given, write a description of the function. Now here, number of vacations are given as x number of postcards by. Now Samantha starts with 10 postcards and every time she goes out on a vacation, she adds 6 postcards so x number of vacations she will add to her collection. So here as the number of vacations will increase, the number of postcards will also increase. So here number of postcards which are represented by the variable y is dependent variable and number of vacations which are represented by the variable x is the independent variable. Now we have to write an equation to represent the number of postcards she will have after x number of vacations. Now from the key idea we know that every linear equation is of the form y is equal to mx plus d where y is the dependent variable and x is the independent variable. Now initially Samantha started with 12 postcards, x number of vacations she will add 6x postcards to her collection. It means the total number of vacations will be y which is equal to 6x plus. So this is the required equation to represent the number of postcards y in terms of number of vacations x is a linear function in slope intercept form. And here slope is equal to coefficient of x which is 6 and y intercept is equal to and now we have to graph the equation. Since we will make table of values for the different values of x and y, now let this be equation number one. Now as x is the independent variable so we will put different values of x in this equation and we will get the corresponding values of y. Now putting equal to 0 in 1 we get y is equal to 6 into 0 plus 12 which implies y is equal to 12. So for x is equal to 0 y is equal to 12. And now putting x is equal to 1 in equation number 1 we get y is equal to 6 into 1 plus 12 which implies y is equal to 6 plus 12 which is equal to 18. So this is equal to 1 we are getting y is equal to, now let us plot the audit pairs 0 12 and 18 on the graph. For this we will take the scale of 1 on x axis and let us plot the other pair 0 12 on the graph. We will take 0 on the x axis and 12 on the y axis. Put a dot here and this is the point which represents the audit pair 0 12. Now the next audit pair that we have to plot is 118. For this we will take 1 on the x axis, 18 on the y axis. This is the required point which represents the audit pair 1 and now we will join these two points by obtaining the graph of the given equation. Now this is the graph of the equation y is equal to 6 x plus 12. The rate of change and initial value. The rate of change is equal to, now the rate of change is equal to 6 to 1 collection in adjudication. Now the initial value is given by the y intercept. So initial is equal to 12. Now we know that y intercept is that value where is 0. Now here you can see that x is equal to 0 in equation 1 we are getting y is equal to 12. It means when number of applications x is equal to 0 then number of postcards y is equal to 12. So number is equal to 12. It means she initially started the collection with planned postcards. She has not gone to any location and this is the solution of the given question. That's all for this session. Hope you all have enjoyed this session.