Question

Wren recorded an outside temperature of –2°F at 8 a.m. When she checked the temperature again, it was 4°F at 12:00 p.m. If x represents the time and y represents the temperature in degrees Fahrenheit, what is the slope of the line through these two data points?

–1.5
–0.5
0.5
1.5

Answer 1

To find the slope of the line through the two data points, we can use the formula for slope:

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

Here, we will assign the points as follows:

- At 8 a.m. (which we can consider as \(x_1 = 0\) hours), the temperature is \(y_1 = -2\) °F.
- At 12 p.m. (which is 4 hours after 8 a.m., so \(x_2 = 4\) hours), the temperature is \(y_2 = 4\) °F.

Substituting these values into the slope formula gives:

\[
m = \frac{4 - (-2)}{4 - 0}
\]
\[
m = \frac{4 + 2}{4}
\]
\[
m = \frac{6}{4}
\]
\[
m = \frac{3}{2}
\]

Thus, the slope \(m\) is \(1.5\).

Therefore, the slope of the line through these two data points is:

**1.5**