Question

write an equation to represent this line. first, write an equation in words to represent the relationship between the volume in the cylinder and the number of marbles. slope: 4 vertical intercept: 6

Explanation:

Step1: Identify word equation structure

The total volume equals the volume added by marbles plus the starting volume.

Step2: Map to slope-intercept form

Slope ($4$) = volume per marble, intercept ($6$) = initial volume. The slope-intercept formula is $y=mx+b$, so substitute $y=v$ (volume), $m=4$, $x$ (marble count), $b=6$.

Answer:

Word Equation:

$\text{volume} = \text{volume of marbles} + \text{initial volume}$

Linear Equation:

$v = 4x + 6$