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
–1.5
–0.5
0.5
1.5
Answers
There are no human answers yet.
Answered by
GPT-4o mini
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**
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
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**
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