Question
The graph shows the linear relationship between the number of pancakes on a plate and the total weight of the plate of pancakes.
What does b=3.5 represent in this problem?
x
y
(1,5)(3,8)
0
1
2
3
4
5
0
1
2
3
4
5
6
7
8
9
10
11
12
Number of pancakes
Total weight (oz)
y = 1.5x + b
5 = 1.5ยท1 + b
b = 3.5
Each pancake weighs 3.5 ounces.
The initial value, or the weight of the
plate when no pancakes are
on it, is 3.5 ounces.
What does b=3.5 represent in this problem?
x
y
(1,5)(3,8)
0
1
2
3
4
5
0
1
2
3
4
5
6
7
8
9
10
11
12
Number of pancakes
Total weight (oz)
y = 1.5x + b
5 = 1.5ยท1 + b
b = 3.5
Each pancake weighs 3.5 ounces.
The initial value, or the weight of the
plate when no pancakes are
on it, is 3.5 ounces.
Answers
GPT-4o mini
In the context of the problem you provided, \( b = 3.5 \) represents the **y-intercept** of the linear equation \( y = 1.5x + b \). This means that when the number of pancakes on the plate (\( x \)) is zero, the total weight of the plate of pancakes (\( y \)) is 3.5 ounces.
In practical terms, this indicates that the plate itself weighs 3.5 ounces when there are no pancakes on it. The coefficient \( 1.5 \) in the equation indicates that each pancake adds an additional 1.5 ounces to the total weight. Therefore, the complete interpretation of \( b = 3.5 \) is that it accounts for the base weight of the plate before any pancakes are added.
In practical terms, this indicates that the plate itself weighs 3.5 ounces when there are no pancakes on it. The coefficient \( 1.5 \) in the equation indicates that each pancake adds an additional 1.5 ounces to the total weight. Therefore, the complete interpretation of \( b = 3.5 \) is that it accounts for the base weight of the plate before any pancakes are added.