The graph shows the linear relationship between the number of pancakes on a plate and the total weight of the plate of pancakes.

Question

Now, solve for the value of b, or the vertical intercept.
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)
8
=
1.5·3+b

b
=

Answer 1

To find the value of \( b \) (the vertical intercept), we need the equation of the line in the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

From the points given, we can find the slope \( m \) using the two points \( (1,5) \) and \( (3,8) \):

1. Find the slope \( m \): \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8 - 5}{3 - 1} = \frac{3}{2} = 1.5 \]

2. Now, we will use one of the points to solve for \( b \). Let's use the point \( (1, 5) \): \[ y = mx + b \] Plugging in the values, we have: \[ 5 = 1.5(1) + b \] \[ 5 = 1.5 + b \] Now, solve for \( b \): \[ b = 5 - 1.5 = 3.5 \]

Thus, the value of \( b \) (the vertical intercept) is: \[ \boxed{3.5} \]