Question

ms. joseph is dropping marbles into a cylinder one at a time. she records the volume of whats in the cylinder after each marble is dropped in. lets write an equation to show the relationship between v, the volume in the cylinder, and x, the number of marbles. start by writing the value of the initial volume in the cylinder. slope: 2 vertical intercept: 10 volume = initial volume + volume of marbles v = \square + ?

Explanation:

Step1: Identify initial volume

The vertical intercept (when $x=0$, no marbles) is the initial volume, so initial volume = 10.

Step2: Define volume per marble

The slope represents volume added per marble, which is 2. For $x$ marbles, total volume added is $2x$.

Step3: Build volume equation

Combine initial volume and marble volume: $v = \text{initial volume} + \text{volume of marbles}$
<Expression>
$v = 10 + 2x$
</Expression>

Answer:

Initial volume: 10
Final equation: $v = 10 + 2x$