This equation shows the linear relationship between the number of minutes since Micah started heating a pot of water and the temperature of the water. x represents the number of minutes, and y represents the temperature in degrees Celsius.

Question

Now, solve for the value of b, or the vertical intercept.
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 need to find the slope \( m \) and then use one of the points given.

From the points provided, we have:

• Point 1: \( (2, 40) \)
• Point 2: \( (4, 60) \)

First, let's calculate the slope \( m \) using the formula:

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

Using the points \( (2, 40) \) and \( (4, 60) \):

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

Now we have the slope \( m = 10 \).

Next, we can use one of the points to solve for \( b \). Let's use the point \( (2, 40) \):

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

So the value of \( b \), the vertical intercept, is \( 20 \).