Raj has a debt of \( \$ 4,100 \) to pay off with no interest added. If he pays \( \$ 50 \) each month, how long will it take him to pay back the loan? The equation can be written as: \( y=-50 x+4,100 \) Solve the problem by solving for the x-intercept. \( \begin{array}{ll}\text { a.) } 89 \text { months } \\ \text { b.) } 82 \text { months } \\ \text { c.) } 74 \text { months } \\ \text { d.) } 67 \text { months }\end{array} \)

To find the time it will take Raj to pay off his debt, we can determine the x-intercept of the equation \( y = -50x + 4,100 \). The x-intercept occurs when \( y = 0 \): \[ 0 = -50x + 4,100 \] Now, solve for \( x \): \[ 50x = 4,100 \] \[ x = \frac{4,100}{50} = 82 \] So, Raj will take 82 months to pay off the loan. The answer is \( \text{b.) } 82 \text{ months} \). In this case, Raj's journey of paying off debt can be compared to a marathon rather than a sprint! Keeping a steady monthly payment is key, and just as running takes endurance and planning, so does paying off debt. By sticking to his payment schedule, he knows he's getting closer to crossing that finish line! When tackling debts, it's common to underestimate how long it might take to clear them. Setting aside a specific amount each month is great, but also focus on budgeting for life’s unexpected expenses. Ensure there’s wiggle room in your budget so that when surprises pop up, you can stay on track without derailing your goal to be debt-free!