 Hello and welcome to the session. In this session we will discuss the question which says that compare the two linear functions given below and determine which has a negative slope. Function one, Kate starts with $30 on a gift card for the bookstore. She spends $1.50 per week to buy a magazine. Let Y be the remaining amount as a function of the number of weeks X. Function two, the school bookstore rents graphene calculators for $4 per month. It also collects a non-refundable yearly fee of $10 for the school. Y is the rule for the total cost C of printing a calculator as a function of the number of months N. Now before starting the solution of this question, we should know a result. And that is when the dependent variable Y decreases will increase in independent variable X then slope is negative and when the dependent variable Y increases with increase in the independent variable X then this result will work out as a key idea for solving out the given question. Now let us start with the solution of the given question. Now in the question we have given two linear functions with different representations. One is in table and the other is in statement form. Now we have to compare these two given linear functions regarding their slopes and here we have to find that which function has a negative slope. Now in function one we have given a table showing number of weeks amount and so Y shows the remaining amount as a function of number of weeks X. So here Y is a function of X. So here Y is the dependent variable and X is the independent variable. Now from the table you can see that when number of weeks is equal to zero then amount is equal to $30 and going on such a way when number of weeks is equal to four then amount is equal to $12 that with increase in value of X there is a decrease in value of Y $30 and spends money each week the amount of money left decreases each week. Now we know that when the dependent variable decreases with the increase in independent variable then slope is negative. So here as Y decreases with the slope she spends $4.50 so slope is equal to minus four point. Now we can also calculate the slope of this table. Now as you can see that change in Y is minus four point five zero and change in X is one. Now slope is equal to change in Y upon change in X. So this is equal to minus four point five zero upon one which is equal to minus four point five zero. From this table we have got the slope as minus four point five zero. Now in function two students pay an yearly non-defendable fee of $12 for rent of the calculator and pay $4 per month so in function two in number of months the total cost of the rent also increases and from the key idea we know that when Y increases that is when the dependent variable increases with increase in the independent variable X then slope is positive and here as the students have to pay the slope will be equal to four. We have to write the rule C of rent of the calculator as a function of the number of months and so here linear function is given by this means E of renting is equal to cost paid per month which is $4 into number of months and per year which is $12 and here slope is positive slope is minus four point five slope is equal to four. Thus function one should have the given question and that's all for this session. Hope you all have enjoyed this session.