Question
Slope:
meaning of the slope:
time (h) 5 10 15 20
Distance (mi) 6 12 18 24
meaning of the slope:
time (h) 5 10 15 20
Distance (mi) 6 12 18 24
Answers
GPT-4o mini
In the context of the data provided, the slope represents the rate of change of distance with respect to time. To understand this more clearly, let's start by looking at the values given:
- At 5 hours, the distance is 6 miles.
- At 10 hours, the distance is 12 miles.
- At 15 hours, the distance is 18 miles.
- At 20 hours, the distance is 24 miles.
The distance increases as time increases. We can calculate the slope (rate of change) using the formula for slope \( m \):
\[
m = \frac{\text{change in distance}}{\text{change in time}} = \frac{\Delta y}{\Delta x}
\]
Using two points from your data, for example (5, 6) and (10, 12):
\[
m = \frac{12 - 6}{10 - 5} = \frac{6}{5} = 1.2
\]
You can also use other pairs of points, and you will find that the slope remains constant. For example, using (10, 12) and (15, 18):
\[
m = \frac{18 - 12}{15 - 10} = \frac{6}{5} = 1.2
\]
This shows that the distance increases by 1.2 miles for every hour that passes. Therefore, the meaning of the slope in this context is that the object is traveling at a constant speed of 1.2 miles per hour.
- At 5 hours, the distance is 6 miles.
- At 10 hours, the distance is 12 miles.
- At 15 hours, the distance is 18 miles.
- At 20 hours, the distance is 24 miles.
The distance increases as time increases. We can calculate the slope (rate of change) using the formula for slope \( m \):
\[
m = \frac{\text{change in distance}}{\text{change in time}} = \frac{\Delta y}{\Delta x}
\]
Using two points from your data, for example (5, 6) and (10, 12):
\[
m = \frac{12 - 6}{10 - 5} = \frac{6}{5} = 1.2
\]
You can also use other pairs of points, and you will find that the slope remains constant. For example, using (10, 12) and (15, 18):
\[
m = \frac{18 - 12}{15 - 10} = \frac{6}{5} = 1.2
\]
This shows that the distance increases by 1.2 miles for every hour that passes. Therefore, the meaning of the slope in this context is that the object is traveling at a constant speed of 1.2 miles per hour.