https://r2.erweima.ai/mathbot/image/17262525878032wan1y8v.jpg

Let's work through the given tasks.

### Instructions:
1. **Find the slope** (pendiente), **y-intercept** (intercepto con el eje \( y \)) and **explicit equation** of the line from the graphs in problems 24 to 27.
2. **GeoGebra tasks** (a and b): Use the slope to identify another point on the line.

#### Let's start with problems 24–27:

### 24. Graph Analysis
- The line crosses the \( y \)-axis at \( y = 10 \) (this is the y-intercept).
- The slope (pendiente) is calculated as the rise over run. Between two clear points, such as (0, 10) and (2, 0), the slope \( m \) is:
  \[
  m = \frac{0 - 10}{2 - 0} = -5
  \]
- The equation of the line is in the form \( y = mx + b \):
  \[
  y = -5x + 10
  \]

### 25. Graph Analysis
- The line passes through the origin \( (0, 0) \), so the \( y \)-intercept is 0.
- Slope: Between points like (0, 0) and (2, 2):
  \[
  m = \frac{2 - 0}{2 - 0} = 1
  \]
- The equation:
  \[
  y = x
  \]

### 26. Graph Analysis
- The y-intercept is at \( y = 2 \).
- The slope can be calculated between points like (0, 2) and (2, -2):
  \[
  m = \frac{-2 - 2}{2 - 0} = -2
  \]
- The equation:
  \[
  y = -2x + 2
  \]

### 27. Graph Analysis
- The y-intercept is at \( y = 1 \).
- Slope calculation from points like (0, 1) and (2, 3):
  \[
  m = \frac{3 - 1}{2 - 0} = 1
  \]
- The equation:
  \[
  y = x + 1
  \]

### Now, for GeoGebra tasks (a and b):
You are provided with the slope \( m \) and must use it to locate a second point and write the equation.

#### a. Slope \( m = -2 \)
- Start at the origin or another point like \( (0, 0) \).
- Moving with the slope: If \( m = -2 \), for every unit right, move two units down. So, the next point is \( (1, -2) \).
- Equation: 
  \[
  y = -2x
  \]

#### b. Slope \( m = -3 \)
- Starting from the origin again, for slope \( m = -3 \), for each unit to the right, move three units down.
- Another point: \( (1, -3) \).
- Equation:
  \[
  y = -3x
  \]

Would you like a detailed explanation of any specific part? Here are some related questions you could explore:

1. What is the significance of the slope in the context of a line?
2. How do we determine the slope if the y-intercept is unknown?
3. Can a line have a slope of zero? If so, what does that mean geometrically?
4. How can you graph a line if you're given just the slope and a point?
5. What happens to the equation of the line if the slope is positive versus negative?

**Tip:** When working with slopes, remember that a positive slope means the line is rising from left to right, and a negative slope means it is falling.

Determine the slope, y-intercept, and explicit equation of the lines in the graphs provided.

Learn how to determine the slope, y-intercept, and explicit equation of lines from graphs. This problem covers key algebraic concepts including the slope formula and linear equations, suitable for students in Grades 8-10.

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