https://r2.erweima.ai/mathbot/image/1726722757064ql9am752.jpg

Let's analyze the graph and the questions provided in the image.

The graph shows the distance Alejandro traveled (in kilometers) over time (in hours). The line is linear, indicating a constant speed.

1. **Question (a)**: _¿Cuánto aumenta la distancia por cada hora desde que Alejandro cruzó el puente?_
   - This is asking for how much the distance increases each hour, which is equivalent to the speed Alejandro is traveling.
   - To calculate this, we need to find the slope of the line in the graph.

2. **Question (b)**: _¿Cuál es la pendiente de la recta?_
   - This asks directly for the slope of the line (the rate of change in distance per hour).

### Calculation of the Slope:
The slope \( m \) is calculated as:
\[
m = \frac{\Delta y}{\Delta x} = \frac{\text{Change in distance}}{\text{Change in time}}
\]
From the graph:
- At \( t = 0 \) hours, \( d = 0 \) km.
- At \( t = 4 \) hours, \( d = 300 \) km.

Thus, the slope (and the speed) is:
\[
m = \frac{300 \, \text{km} - 0 \, \text{km}}{4 \, \text{h} - 0 \, \text{h}} = \frac{300 \, \text{km}}{4 \, \text{h}} = 75 \, \text{km/h}
\]

### Answers:
(a) The distance increases by **75 kilometers per hour**.
(b) The slope of the line is **75**.

Would you like more details or have any further questions?

Here are 5 related questions to expand the topic:
1. How can the slope of a line be interpreted in other real-life situations?
2. What happens if the slope of the line is negative?
3. How would the graph change if Alejandro's speed doubled?
4. What is the total distance Alejandro would travel after 6 hours at the same speed?
5. Can you describe how to find the y-intercept in a linear equation?

**Tip**: Always check the units on the graph to ensure proper slope calculations when working with real-life data.

¿Cuánto aumenta la distancia por cada hora desde que Alejandro cruzó el puente? ¿Cuál es la pendiente de la recta?

Learn how to calculate the slope of a line on a distance-time graph, showing Alejandro's constant speed. The problem involves determining how much the distance increases per hour and calculating the slope of the line. Suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation