Question

jane is saving to buy a new gaming system. the function graphed below shows the amount of money, $s(x)$ (in dollars), that jane has left to save after $x$ weeks of saving.

find $s(9)$ and interpret this value.
(a) $s(9) = \square$
(b) the answer to part (a) means that after jane has been saving for $\square$ weeks, she has $\\$\square$ left to save.

Explanation:

Step 1: Determine the equation of the line

From the graph, we can see that the line passes through (0, 360) and (18, 0). The slope \( m \) is \( \frac{0 - 360}{18 - 0} = -20 \). Using the slope-intercept form \( y = mx + b \), with \( b = 360 \), the equation is \( S(x) = -20x + 360 \).

Step 2: Calculate \( S(9) \)

Substitute \( x = 9 \) into the equation: \( S(9) = -20(9) + 360 = -180 + 360 = 180 \).

Answer:

(a) \( S(9) = \boxed{180} \)

(b) The answer to part (a) means that after Jane has been saving for \( \boxed{9} \) weeks, she has \( \$ \boxed{180} \) left to save.