Question

The temperature of a substance was recorded over several minutes, as shown in the graph below. The graph displays the linear relationship between the temperature (measured in degrees Celsius) and the number of minutes the substance was being observed.
Temperature Over Time
Temperature (°C)
Time (Minutes)
dot at 2 on the y-axis and a dot that intersects at 12 y-axis and 8 x-axis


Which statement best describes the slope of the graph?

Responses
A The temperature is increasing 3.25°C each minute.The temperature is increasing 3.25°C each minute.
B The temperature is increasing 5.25°C each minute.The temperature is increasing 5.25°C each minute.
C The temperature is increasing 1.25°C each minute.The temperature is increasing 1.25°C each minute.
D The temperature is increasing 7.25° C each minute.

Answer 1

To determine the slope of the graph, we can use the two points given:

1. The first point is (0, 2) which represents the temperature of 2°C at 0 minutes.
2. The second point is (8, 12) which represents the temperature of 12°C at 8 minutes.

The slope (m) of a line is calculated using the formula:

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

Plugging the values into the formula:

- \(y_2 = 12\) (the temperature at 8 minutes)
- \(y_1 = 2\) (the temperature at 0 minutes)
- \(x_2 = 8\) (the time at which the temperature is 12°C)
- \(x_1 = 0\) (the initial time)

\[
m = \frac{(12 - 2)}{(8 - 0)} = \frac{10}{8} = 1.25
\]

So the slope of the graph is \(1.25\) °C per minute.

Thus, the best description of the slope of the graph is:

C. The temperature is increasing 1.25°C each minute.