Question

a bowl starts with 7 milliliters of water in it. kelly is dropping marbles into the bowl one at a time. she records the volume in the bowl after each marble is dropped in. the graph below shows the relationship between the number of marbles and the volume in the bowl. remember, the slope is the change in vertical distance for a given change in horizontal distance. we can use any two points on the line to find the slope. label the coordinates of the two points on the graph below. slope = \\(\frac{\text{vertical distance}}{\text{horizontal distance}}\\)

Explanation:

Step1: Identify first point coordinates

The first point (0 marbles, initial volume) is $(0, 7)$.

Step2: Identify second point coordinates

The second point (3 marbles, volume) is $(3, 16)$.

Step3: Calculate vertical distance

Subtract initial y-value from final y-value.
$16 - 7 = 9$

Step4: Calculate horizontal distance

Subtract initial x-value from final x-value.
$3 - 0 = 3$

Step5: Compute the slope

Divide vertical by horizontal distance.
$\text{slope} = \frac{9}{3} = 3$

Answer:

Labeled coordinates: $(0, 7)$ and $(3, 16)$
Slope: $3$ milliliters per marble