The graph shows the linear relationship between the number of minutes since Micah started heating a pot of water and the temperature of the water.

Question

Substitute the slope, 10, for m in our equation.
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)
Slope 0 = 0 10
y 0 = 0 mx+b
y 0 = 0
x+b

Answer 1

Given the problem, we need to write the equation of the line using the slope-intercept form, which is:

\[ y = mx + b \]

where:

• \( m \) is the slope,
• \( b \) is the y-intercept,
• \( x \) is the number of minutes,
• \( y \) is the temperature in °C.

You have specified that the slope \( m \) is 10. So, the equation starts as:

\[ y = 10x + b \]

To find \( b \), we can use one of the points from the graph. You have provided two points: (2, 40) and (4, 60).

Let's use the point (2, 40):

1. Substitute \( x = 2 \) and \( y = 40 \) into the equation: \[ 40 = 10(2) + b \]
2. Solve for \( b \): \[ 40 = 20 + b \] \[ b = 40 - 20 = 20 \]

Now we have both the slope and the y-intercept. We can now write the final equation of the line:

\[ y = 10x + 20 \]

This equation represents the relationship between the number of minutes since Micah started heating the pot of water and the temperature of the water. The temperature increases by 10°C for each additional minute, starting from an initial temperature of 20°C.