Question

the graph shows the relationship between the total amount of money that carly will have left, y, if she buys x packs of baseball cards.

graph: y-axis labeled money left (in $), x-axis labeled packs of cards bought. points at (1,16), (2,12), (3,8), (4,4), (5,0)

how much money will she have if she doesnt buy any packs of baseball cards?

$16
$18
$19
$20

Explanation:

Step1: Identify x=0 case

We need to find the money left when \( x = 0 \) (no packs bought). The graph's y - intercept (when \( x = 0 \)) can be inferred from the pattern or by extending the line. But looking at the points, when \( x = 1 \), \( y = 16 \); \( x = 2 \), \( y = 12 \); \( x = 3 \), \( y = 8 \); \( x = 4 \), \( y = 4 \); \( x = 5 \), \( y = 0 \). The slope is \( \frac{12 - 16}{2 - 1}=- 4 \). Using the point - slope form \( y - y_1=m(x - x_1) \) with \( (x_1,y_1)=(1,16) \) and \( m=-4 \), the equation is \( y-16=-4(x - 1) \). When \( x = 0 \), \( y-16=-4(0 - 1)\Rightarrow y-16 = 4\Rightarrow y = 20 \). Alternatively, we can see the pattern: each time \( x \) increases by 1, \( y \) decreases by 4. So when \( x = 0 \) (1 less than \( x = 1 \)), \( y \) should be 16+4 = 20.

Step2: Confirm the value

By analyzing the linear relationship (the points lie on a straight line with slope - 4) and calculating the y - intercept, we find that when \( x = 0 \) (no packs of baseball cards bought), the money left \( y = 20 \).

Answer:

\$20