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.
Now that you’ve found the slope and the vertical intercept, you can use these two values to help you write an equation that represents the relationship between the volume, v, and the number of marbles, x. Go for it. Write an equation that represents this line.
x
y
0
1
2
3
4
5
0
2
4
6
8
10
12
14
16
Number of marbles, x
Volume in mL, v
slope :
1
2
vertical intercept : 8
equation:
Enter
Now that you’ve found the slope and the vertical intercept, you can use these two values to help you write an equation that represents the relationship between the volume, v, and the number of marbles, x. Go for it. Write an equation that represents this line.
x
y
0
1
2
3
4
5
0
2
4
6
8
10
12
14
16
Number of marbles, x
Volume in mL, v
slope :
1
2
vertical intercept : 8
equation:
Enter
Answers
GPT-4o mini
To write the equation of the line, we can use the slope-intercept form of a linear equation, which is:
\[ v = mx + b \]
where:
- \( v \) is the volume,
- \( m \) is the slope,
- \( x \) is the number of marbles,
- \( b \) is the vertical intercept.
From your information:
- The slope \( m = \frac{1}{2} \)
- The vertical intercept \( b = 8 \)
Substituting these values into the equation gives us:
\[ v = \frac{1}{2}x + 8 \]
So, the equation that represents the relationship between the volume, \( v \), and the number of marbles, \( x \), is:
\[ v = \frac{1}{2}x + 8 \]
\[ v = mx + b \]
where:
- \( v \) is the volume,
- \( m \) is the slope,
- \( x \) is the number of marbles,
- \( b \) is the vertical intercept.
From your information:
- The slope \( m = \frac{1}{2} \)
- The vertical intercept \( b = 8 \)
Substituting these values into the equation gives us:
\[ v = \frac{1}{2}x + 8 \]
So, the equation that represents the relationship between the volume, \( v \), and the number of marbles, \( x \), is:
\[ v = \frac{1}{2}x + 8 \]