Answer:
In Example 2, the relationship between the dependent variable a, the amount still owed, and the independent variable w, the number of weeks Ethan pays $5, is given by the equation:
a = 100 - 5w
If we increase the value of w by 1, then the new value of w becomes w + 1. To find out what happens to the value of the dependent variable a, we substitute w + 1 for w in the equation:
a = 100 - 5(w + 1)
a = 100 - 5w - 5
Simplifying this expression, we get:
a = 95 - 5w
Comparing this expression to the original equation, we see that the value of the dependent variable a decreases by 5 when the value of the independent variable w is increased by 1. Therefore, if Ethan pays $5 for one more week, the amount still owed will decrease by $5.