Question

The graph shows the linear relationship between the number of pancakes on a plate and the total weight of the plate of pancakes.
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)
5
=
1.5·1+b

b
=

Answer 1

To find the vertical intercept \( b \) in the linear equation \( y = mx + b \), we first need to determine the slope \( m \) using the two given points on the graph: \( (1, 5) \) and \( (3, 8) \).

The formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points \( (1, 5) \) and \( (3, 8) \):
- \( x_1 = 1 \), \( y_1 = 5 \)
- \( x_2 = 3 \), \( y_2 = 8 \)

Now let's calculate the slope \( m \):

\[
m = \frac{8 - 5}{3 - 1} = \frac{3}{2} = 1.5
\]

Now that we have the slope, we can use one of the points to solve for \( b \). Let’s use the point \( (1, 5) \).

The equation of a line in slope-intercept form is:

\[
y = mx + b
\]

Substituting in the values we know:

\[
5 = 1.5 \cdot 1 + b
\]

This simplifies to:

\[
5 = 1.5 + b
\]

Now we solve for \( b \):

\[
b = 5 - 1.5
\]

\[
b = 3.5
\]

Thus the value of \( b \) (the vertical intercept) is:

\[
\boxed{3.5}
\]