Question

Diana is trying to pay off a loan. She borrowed $600 and plans on making monthly

payments of $90. Using this information, create an equation written in slope-intercept
form that models the amount owed y of Diana's loan after x months.

Answer 1

Diana's loan amount owed after x months is represented by the equation y = -90x + 600, where y is the amount owed and x is the number of months.

Step-by-step explanation:

To create an equation in slope-intercept form representing the amount Diana owes on her loan after x months, we can use the formula y = mx + b, where y is the amount owed, x is the number of months, m is the slope (change in the amount owed per month), and b is the y-intercept (initial amount owed).

In Diana's case, she starts with a $600 loan and makes monthly payments of $90. Therefore, the amount owed decreases by $90 each month, hence m (the slope) is -90. The initial amount borrowed, which is also the y-intercept, b, is $600.

The equation modeling the amount Diana owes after x months would then be:

y = -90x + 600

Here, each month that passes, Diana pays off an additional $90 of her loan, which is reflected in the negative slope.