Question

the graph shows the relationship between the number of marbles and the volume in a new cylinder. write an equation to represent this line. what does the vertical intercept of 8 mean in this situation? the vertical intercept is the y - value when x is 0, so in this situation, it’s the volume when there are 0 marbles. the volume increases 1 ml for every 8 marbles added. the volume is 8 ml when there are no marbles in the cylinder. the volume increases 8 ml for every 1 marble added.

Explanation:

Step1: Identify vertical intercept

The vertical intercept (y-intercept) is the y-value when $x=0$. From the graph, this is $b=8$.

Step2: Calculate slope

Slope $m = \frac{\text{change in } y}{\text{change in } x}$. When $x=5$, $y=11$. So $m=\frac{11-8}{5-0}=\frac{3}{5}=0.6$.

Step3: Write line equation

Use slope-intercept form $y=mx+b$.
$y = 0.6x + 8$

Step4: Match intercept meaning

The vertical intercept 8 is volume at 0 marbles.

Answer:

Equation: $y = \frac{3}{5}x + 8$
Correct statement about vertical intercept: The volume is 8 mL when there are no marbles in the cylinder.