1. In a linear relationship, the dependant variable changes at a constant rate (up down, or doesn’t change at all) and so does the independent variable. For example, if Sophia starts with $200 but goes shopping every weekend and spends $25 each trip to the mall, the variables will increase and decrease at a steady rate. The two variables in this situation are: the number of weeks (1) and the amount of money Sophia has at the end of the week. (2) As variable 1 increases by 1 week, variable 2 decreases by $25. So both variables either increase or decrease, but at a steady rate.
2. The pattern of change for a linear relationship shows up in a table by the increase or decrease of a number. In a table, the numbers show the pattern of change because you can see the change through the numbers by adding, subtracting, multiplying, or dividing the differences. For example, if we have the same situation with Sophia, the numbers in the table will decrease by 25 as the weeks increase by 1. The pattern of change shows in the graph the data line going completely straight, with coordinates to represent the numbers. If we have the same situation with Sophia her graph would be a straight diagonally downward line. The pattern of change of a linear relationship shows in an equation by being multiplied, divided, etc. by the dependant variable. In the Sophia problem the equation would look like: M= 200-25w. And the pattern change is the 200-25w so it is shown by division, addition, or in this case, multiplication and subtraction to the dependant variable.
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