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. find the change in vertical distance from (0, 8) to (2, 9). slope = \frac{vertical distance}{horizontal distance}

Explanation:

Step1: Calculate vertical change

Subtract initial y-value from final y-value:
$9 - 8 = 1$

Step2: Calculate horizontal change

Subtract initial x-value from final x-value:
$2 - 0 = 2$

Step3: Find the slope

Divide vertical change by horizontal change:
$\text{slope} = \frac{1}{2}$

Step4: Identify y-intercept

The line crosses the y-axis at $(0, 8)$, so $b=8$.

Step5: Write line equation

Use slope-intercept form $y=mx+b$:
$y = \frac{1}{2}x + 8$

Answer:

Change in vertical distance: $1$
Equation of the line: $y = \frac{1}{2}x + 8$