 Hello and welcome to the session. In this session, we are going to discuss the following question which says that Sam has a garden in his house in which he has rose flower plants. The number of red rose flower plants is 2 less than 5 times the number of pink rose flower plants form an equation and represent this relationship on the graph. Now the question says that Sam has a garden in which he has rose flower plants where the number of red rose flower plants is 2 less than 5 times the number of pink rose flower plants. Now we need to form an equation for this relationship and also we shall represent this relationship on the graph. Before forming an equation for the given statement we first identify the independent variables and the dependent variables. Now we shall learn about independent variables and dependent variables. In a system independent variables are taken as inputs which can be given specific values freely and variables that are determined by other variables in the expression or if their values depend on the values of the independent variables are called dependent variables. With this key idea let us move on to the solution. Now the question says that the number of red rose flower plants is 2 less than 5 times the number of pink rose flower plants and we need to form an equation for this relationship. Before we form an equation we have to first identify which is the dependent variable and which is the independent variable. Here the number of rose flower plants depends on the number of pink flower plants. So let the number of pink rose flower plants be x which is the independent variable and let the number of red rose flower plants be y which is the dependent variable and from the key idea we know that independent variables are taken as inputs which can be given specific values freely and the variables that are determined by other variables in the expression are if their values depend on the values of the independent variables are called dependent variables and we have given that number of red rose flower plants is 2 less than 5 times the number of pink rose flower plants. That is we have number of red rose flower plants is equal to 5 into number of pink rose flower plants minus 2 or we can write it as number of red rose flower plants which is denoted by y is equal to 5 into number of pink rose flower plants that is x minus of 2 hence y is equal to 5x minus 2 is the required equation. Now let us draw this on the graph. For this we first draw the table to obtain the ordered pairs. First row of the table is for x, second is for y and third is the row for the resulted ordered pair x, y. Let the values for x be 0, 1 and 2 and if the value of x is 0 and we know that y is given by 5 into x minus 2 that is 5x minus 2 so here we substitute the value of x as 0 and we get 5 into 0 minus 2 which is equal to 5 into 0 is 0 minus 2 that is minus 2 so here we get the value of y as minus 2 so x is equal to 0, y will be equal to minus 2 so the ordered pair obtained as given by 0 minus 2 Now if x is equal to 1 then the value for y will be equal to 5 into 1 minus 2 that is 5 minus 2 which is equal to 3 so we get y is equal to 3 if the value of x is equal to 1 then the value of y is given by 3 and the ordered pair so obtained is 1, 3 and lastly if the value of x is equal to 2 then the value of y will be equal to 5 into 2 minus 2 that is 5 into 2 that is 10 minus 2 which is equal to 8 so we get the value of y as 8 that is if the value of x is equal to 2 then we get the value of y as 8 and the ordered pair is 2, 8 now we shall plot these points on the graph we will draw the perpendicular axis and mark points on it so here we have the horizontal axis and the vertical axis the horizontal axis x represents the independent variables and the vertical axis y will represent the dependent variables now we shall mark the points on this graph first let us take the point 0 minus 2 we mark 0 on the x axis and minus 2 on the y axis and we get the point 0 minus 2 next we mark the point 1, 3 by taking 1 on the x axis and 3 on the y axis and we get the point 1, 3 similarly we mark the point 2, 8 by taking 2 on the x axis and 8 on the y axis and we get the point 2, 8 now we have got all the 3 points on the graph and then we join the 3 points and obtain a straight line by joining these 3 points and this is our required graph this completes our session hope you enjoyed this session