Question

A graph titled Isaac's Experiment has time (minutes) on the x-axis and Temperature (degrees Fahrenheit) on the y-axis. A line goes through points (0, 80) and (2, 70).

A graph titled Sakura's Experiment has time (minutes) on the x-axis and Temperature (degrees Fahrenheit) on the y-axis. A line goes through points (0, negative 80) and (8, 0).

Which statement is correct?
The slope of the graph that represents Isaac’s data is positive, and the slope of the graph that represents Sakura’s data is positive.
The slope of the graph that represents Isaac’s data is positive, and the slope of the graph that represents Sakura’s data is negative.
The slope of the graph that represents Isaac’s data is negative, and the slope of the graph that represents Sakura’s data is positive.
The slope of the graph that represents Isaac’s data is negative, and the slope of the graph that represents Sakura’s data is negative.

Answer 1

To determine the slope of each graph, we can use the formula for slope, which is defined as:

\[
\text{slope} = \frac{\Delta y}{\Delta x}
\]

where \(\Delta y\) is the change in the y-values (Temperature) and \(\Delta x\) is the change in the x-values (time).

**For Isaac's Experiment:**
Points on the line: (0, 80) and (2, 70)

- Change in y (\(\Delta y\)) = 70 - 80 = -10
- Change in x (\(\Delta x\)) = 2 - 0 = 2

Now, calculating the slope:
\[
\text{slope} = \frac{-10}{2} = -5
\]

So, the slope of Isaac's graph is negative.

**For Sakura's Experiment:**
Points on the line: (0, -80) and (8, 0)

- Change in y (\(\Delta y\)) = 0 - (-80) = 80
- Change in x (\(\Delta x\)) = 8 - 0 = 8

Now, calculating the slope:
\[
\text{slope} = \frac{80}{8} = 10
\]

So, the slope of Sakura's graph is positive.

Now let's review the options given:

1. The slope of the graph that represents Isaac’s data is positive, and the slope of the graph that represents Sakura’s data is positive. **(Incorrect)**
2. The slope of the graph that represents Isaac’s data is positive, and the slope of the graph that represents Sakura’s data is negative. **(Incorrect)**
3. The slope of the graph that represents Isaac’s data is negative, and the slope of the graph that represents Sakura’s data is positive. **(Correct)**
4. The slope of the graph that represents Isaac’s data is negative, and the slope of the graph that represents Sakura’s data is negative. **(Incorrect)**

The correct statement is:
**The slope of the graph that represents Isaac’s data is negative, and the slope of the graph that represents Sakura’s data is positive.**