 Hello and welcome to the session. In this session, we will learn how to find values from a linear function in terms of the situation it models and in terms of table of values. Now in our earlier session, we have discussed the way of writing linear function to find initial value and rate of change and here we will discuss how to find values from relation and make graph and table of values. Now we know that linear function is represented in y is equal to nx plus b form. Now to find values of y from this function, we assign values to x same values of y. Similarly, for a particular value of y, we can obtain the corresponding value of x by putting the value of y in the given function. And when we draw an input output table for the values of x and y, that table of values and this table of values gives us the ordered pairs y which we can plot on the coordinate plane and draw the graph of the function which will be a straight line. And we can obtain initial value from graph by looking at y intersect 0b. Now we know that y intersect is that point where the graph of linear function cuts the y axis and slope of line will give us the rate of change. Now let us discuss an example. Justin has $54 to buy books at library. People got books while cohesion. y is equal to 54 minus 3x represents the amount of money left over if she buys x paperback books. And let us find that how much money is left if she buys each paperback books. Now here y represents left over money and x represents number of paperback books that relation between them is given by y is equal to 54 minus. Now here we have to find that how much money is left if she buys each paperback books. It means for x is equal to 8 we have to find the value of y. Now let this be equation number one. So putting equation one we get y is equal to 54 minus 3 into 8 which is equal to 54 minus 24 which is equal to 30. It means when she buys 8 books she is left with $30. Now if she has $27 left paperback books that she buys it means here y is given to us as $27 and for y is equal to 27 we have to find the value of n. Putting y is equal to equation one we get 27 is equal to 54 minus 3x which further is 54 is equal to minus 3x and this gives minus 27 is equal to minus 3x and further this implies 1 3 which is equal to when $27 were left she had bought 9 paperback books. Now the next part let us make a table of values showing left over money for various number of paperback books she bought. Now to make table of values we will assign the values of x and we will obtain corresponding values of y. It means we will push different values of x in this relation and we will obtain the corresponding values of y. Now first of all let us put in this relation and here we will obtain y is equal to 54 minus 3 into 1 which is equal to 54 minus 3 so minus 3 is 51. Then we will put x is equal to 2 for x is equal to 2 y is equal to 54 minus 3 into 2 which is equal to 54 minus 6 and this is equal to 48. We obtain the corresponding values of y. So here we have obtained the table of values for more money for various number of paperback books she bought. And now we have to get what is the initial amount of money. Now to find the initial value we assign now when Jasmine did not buy any book you apply will be the initial amount. So here when x is equal to 0 this equation that is the equation number 1 to 0 in equation 1 we get y is equal to 54 minus 3 into 0 which is equal to 54 minus 0 which is equal to 54. 54 dollars. Now the next part we have to draw the graph of the function. Now in bar D we have obtained the ordered pairs 0, 54 that is when x is equal to 0 y is equal to 54. So this is the ordered pairs 0, 54. Now as we are in the graph we will take this ordered pair we will take the ordered pairs from the table of values which we have obtained in this graph scheme of 6 on y axis. First of all we will put a dot on the initial value equal to 0 then we have obtained the initial value that is y is equal to 54 dot on this initial value given by the intersect 54. Now let us plot the other ordered pairs from this table in this table where x is equal to 1, y is equal to 51. So the first ordered pair is 151. Similarly the second ordered pair is 2 and now we will plot all these ordered pairs on the graph. Now here we have plotted all the ordered pairs here this is the point which represents the ordered pair 0, 54 this is the point which represents the ordered pair 151 which represents the ordered pair 3, 45 and next this point represents the ordered pair which represents the ordered pair and now we will join all these points. Now joining all these points we obtain a straight line function y is equal to 54 minus. Now let us find rate of change or slope of this line from the graph. For this we will take any two points which lie on this line these two points slope is equal to change in y upon now change in y is 54 minus 48 whole upon change in x is 0 minus 2. So this is equal to 6 upon minus 2 which is equal to slope of this line which represents option y is equal to 54 minus 38 in the set is 54. In this session we have learnt how to find values from relation and main graph and table of values. So this completes our session hope you all have enjoyed the session.