Question

if a linear function modeling savings has a y-intercept of $50, what does this mean?

a. the person will never have more than $50.

b. the person starts with $50.

c. the person saves $50 every month.

d. the person owes $50.

Explanation:

In a linear function \( y = mx + b \) modeling savings, the y - intercept (\( b \)) represents the value of \( y \) when \( x = 0 \). Here, \( x \) can represent time (e.g., number of months) and \( y \) represents savings. When \( x = 0 \) (at the start, before any time has passed), \( y=b = 50 \). So this means the person starts with $50. Option a is wrong because the slope could be positive (increasing savings) or negative (decreasing), so they might have more than $50. Option c describes the slope (rate of saving per month), not the y - intercept. Option d is incorrect as savings of $50 is not an owed amount.

Answer:

b. The person starts with $50.