Question

What's the Error? Three months after buying a computer, Jim owed

$1000. Six months after buying the computer, Jim owed $550. Jim said
the equation y = 150x + 100 represents the situation. Describe Jim's
error and write the correct equation.​

Answer 1

y = -150x + 1450

Explanation:

y is Jim's amount that he owes and x is the number of months

First, Jim's equation says that it starts at $100 owed and increases at $150 each month. This can't be true because we are given the points (3, 1000) and (6, 550), which show a negative slope and therefore the amount owed must be decreasing in reality. Therefore we can flip the sign on the slope and find the correct y-intercept which would represent how much he owed for the computer when he bought it.

y = -150x + b

1000 = -150(3) + b

1000 = -450 + b

b = 1450

Therefore, the true situation is that Jim bought a computer and owed $1450 from the start. Each month, he pays off $150 and therefore the amount of debt decreases.

Correct Equation: y = -150x + 1450