It will take Amelia 30 months to pay back the loan by making monthly payments of $1,700.
How to solve the problem
To solve the problem by finding the x-intercept of the equation, set y = 0 and solve for x. In this case, y represents the remaining debt, and x represents the number of months it takes to pay back the loan.
The equation given is:
y = -1,700x + 51,000
Setting y = 0, we have:
0 = -1,700x + 51,000
To solve for x, isolate the variable:
1,700x = 51,000
Dividing both sides of the equation by 1,700:
x = 51,000 / 1,700
Simplifying this division, we find:
x = 30
Therefore, it will take Amelia 30 months to pay back the loan by making monthly payments of $1,700.