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

What is the slope of this line?
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
y 0 = 0 mx+b

Answer 1

To find the slope of the line that represents the relationship between the number of minutes since Micah started heating the pot of water (x-axis) and the temperature (y-axis), we can use the two points provided: (2, 40) and (4, 60).

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

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

Substituting the coordinates of the points:

\((x_1, y_1) = (2, 40)\)

\((x_2, y_2) = (4, 60)\)

Now plug in the values:

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

Therefore, the slope of the line is 10. This means for every minute that passes, the temperature of the water increases by 10 degrees Celsius.