Final answer:
To model Zachary's balance after x months on a payment plan for a computer, we use the equation y = -110x + 1820, where y is the balance and x is the number of months since the purchase.
Step-by-step explanation:
Zachary purchases a computer for $1,600 on a payment plan. The balance after four months and six months can be used to solve the mathematical problem completely by creating a linear equation that models the balance, y, after x months. To establish this equation, we recognize from the information provided that the balance decreased by $220 between the fourth and sixth months (from $1380 to $940). Assuming that the payment amount is fixed and consistent over the time, this gives us a rate of change of $220 over 2 months, or $110 per month.
We can now setup the equation with two known points. The point (4, 1380) represents the balance after four months, and the point (6, 940) represents the balance after six months. Using the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept, we can first find the slope m which is -110 (the amount the balance decreases each month).
Now we can use one of the points to find the value of b. Plugging in the values from the point (4, 1380) into the equation, we get:
1380 = -110(4) + b, which simplifies to:
1380 = -440 + b
1820 = b
So y = -110x + 1820 is the equation that models Zachary's balance after x months.