Question

problems 9–10
in aesop’s fable “the crow and the pitcher,” a thirsty crow discovers a pitcher of water but is unable to reach the water with its beak. so the crow adds pebbles to the pitcher to make the water rise higher and higher until it reaches the top. then it can drink the water!
thiago recreates this situation using a cylinder containing water and a bunch of marbles. the line represents the volume of the cylinder’s contents, ( y ), after ( x ) marbles are added.
what is the slope of the line?

Explanation:

Step1: Identify two points on the line

Assume from the graph, when \( x = 0 \) (no marbles), \( y = 20 \) mL (initial volume). When \( x = 10 \) marbles, \( y = 100 \) mL (final volume). (We can also use other clear points, but these are typical from such graphs.)

Step2: Use slope formula \( m=\frac{y_2 - y_1}{x_2 - x_1} \)

Substitute \( (x_1,y_1)=(0,20) \) and \( (x_2,y_2)=(10,100) \) into the formula. So \( m=\frac{100 - 20}{10 - 0}=\frac{80}{10} = 8 \). Wait, maybe the initial volume is different. Wait, looking at the graph, maybe when \( x = 0 \), \( y = 20 \), and when \( x = 10 \), \( y = 100 \)? Wait, no, maybe the grid. Let's re - check. Suppose the line passes through (0, 20) and (10, 100). Then slope is \( \frac{100 - 20}{10 - 0}=8 \). Or maybe (0, 20) and (5, 60). Then \( \frac{60 - 20}{5 - 0}=\frac{40}{5}=8 \). So the slope is 8. Wait, maybe the initial volume is 20, and each marble adds 8 mL? Wait, let's think again. The slope represents the change in volume per marble. So if we take two points, say when \( x = 0 \), \( y = 20 \) (volume without marbles) and when \( x = 10 \), \( y = 100 \) (volume with 10 marbles). Then the change in \( y \) is \( 100 - 20 = 80 \), change in \( x \) is \( 10 - 0 = 10 \). So slope \( m=\frac{80}{10}=8 \). So the slope is 8, meaning each marble adds 8 mL to the volume.

Answer:

8