Question

slope: 4
vertical intercept: 6
volume = initial volume + volume of marbles
v = 6 + 4x
v = 6 + 4·9
v = 6 + 36
v = 42
the volume in the cylinder would be 9 ml if there were 42 marbles.
the volume in the cylinder is 42 ml when there are no marbles.
the volume in the cylinder would be 42 ml if there were 9 marbles.

Explanation:

1. Analyze the given linear equation $V = 6 + 4x$, where $V$ = total volume (mL) and $x$ = number of marbles.
2. Evaluate each statement:

• First statement: Claims $V=9$ when $x=42$. Substituting $x=42$ gives $V=6+4(42)=174$, which is incorrect.
• Second statement: Claims $V=42$ when $x=0$ (no marbles). Substituting $x=0$ gives $V=6+4(0)=6$, which is incorrect.
• Third statement: Claims $V=42$ when $x=9$. Substituting $x=9$ gives $V=6+4(9)=6+36=42$, which matches the calculation shown and is correct.

Answer:

The volume in the cylinder would be 42 mL if there were 9 marbles.