Question

a bucket starts with 6 milliliters of water in it. cameron is dropping marbles into the bucket one at a time. he records the volume in the bucket after each marble is dropped in. the graph below shows the relationship between the number of marbles and the volume in the bucket. 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. \\(\text{slope} = \frac{\text{vertical distance}}{\text{horizontal distance}}\\)

Explanation:

Step1: Identify first point coordinates

The first point is at $x=0$ (0 marbles) and $y=6$ (6 mL), so coordinates are $(0, 6)$.

Step2: Identify second point coordinates

The second point is at $x=3$ (3 marbles) and $y=18$ (18 mL), so coordinates are $(3, 18)$.

Step3: Calculate vertical distance

Subtract initial y-value: $18 - 6 = 12$

Step4: Calculate horizontal distance

Subtract initial x-value: $3 - 0 = 3$

Step5: Compute slope

Divide vertical by horizontal: $\frac{12}{3} = 4$

Answer:

Labeled coordinates:

• Lower point: $(0, 6)$
• Upper point: $(3, 18)$

Slope: $4$