Now, solve for the value of b, or the vertical intercept.

Question

x
y
(4,60)
(2,40)
0
2
4
6
8
10
12
0
20
40
60
80
100
120
140
Number of minutes
Temperature (°C)
60
=
10·4+b

b
=

Answer 1

To solve for the vertical intercept \( b \) in the equation \( y = mx + b \), we first need to identify the slope \( m \) of the line using the given points. We have two points: \( (4, 60) \) and \( (2, 40) \).

1. Calculate the slope \( m \) using the formula:

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

Using the points \( (x_1, y_1) = (2, 40) \) and \( (x_2, y_2) = (4, 60) \):

\[ m = \frac{60 - 40}{4 - 2} = \frac{20}{2} = 10 \]

Now that we have the slope \( m \), we can use one of the points to calculate the intercept \( b \). We can use the point \( (2, 40) \):

2. Plug the point \( (2, 40) \) into the equation \( y = mx + b \):

\[ 40 = 10(2) + b \] \[ 40 = 20 + b \]

3. Solve for \( b \):

\[ b = 40 - 20 = 20 \]

Thus, the vertical intercept \( b \) is:

\[ \boxed{20} \]