Question

jina is saving to buy a new gaming system. the function graphed below shows the amount of money, s(x) (in dollars), that jina has left to save after x weeks of saving.
find s(6) and interpret this value.
(a) s(6) =
(b) the answer to part (a) means that after jina has been saving for weeks, she has $ left to save.

Explanation:

Step1: Determine the slope of the line

From the graph, when \( x = 0 \), \( S(0)=360 \) (y - intercept), and we can find another point. Let's assume the line goes from \( (0, 360) \) to, say, when \( x = 12 \), maybe \( S(12)=120 \) (estimating from the graph's scale). The slope \( m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{120 - 360}{12 - 0}=\frac{- 240}{12}=-20 \). So the equation of the line is \( S(x)=- 20x + 360 \) (using slope - intercept form \( y=mx + b \), where \( m=-20 \) and \( b = 360 \)).

Step2: Calculate \( S(6) \)

Substitute \( x = 6 \) into the equation \( S(x)=-20x + 360 \).
\( S(6)=-20\times6 + 360 \)
\(=-120 + 360 \)
\( = 240 \)

Answer:

(a) \( S(6)=\boxed{240} \)
(b) The answer to part (a) means that after Jina has been saving for \( \boxed{6} \) weeks, she has \( \boxed{240} \) left to save.