https://r2.erweima.ai/mathbot/image/1726614860187tmlwyszh.jpg

Let's start solving the exercises in **Actividad 1.3.4** from the image you uploaded.

### EJERCICIO 1:
For each pair of points, calculate the slope and then the equation of the line in both point-slope and general form.

The slope formula is:

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

Then, the point-slope form of the line is:

\[
y - y_1 = m(x - x_1)
\]

After that, rearrange the equation to general form:

\[
Ax + By + C = 0
\]

#### a. \( P(-2, -2), Q(-1, 0) \)
- Slope: 
\[
m = \frac{0 - (-2)}{-1 - (-2)} = \frac{2}{1} = 2
\]
- Point-slope form: 
\[
y + 2 = 2(x + 2)
\]
- General form: 
\[
y = 2x + 2 \quad \Rightarrow \quad 2x - y + 2 = 0
\]

I will continue solving the rest of the problems if you're ready. Would you like more details or explanations?

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Here are 5 related questions that expand on these topics:

1. How do you derive the general equation of a line from two points?
2. What does the slope represent geometrically in a line?
3. Can a line have an undefined slope, and what does it look like?
4. How does the general form of a line help in identifying the slope and intercept?
5. What are the conditions for two lines to be parallel or perpendicular?

**Tip:** When calculating the slope, always be mindful of signs, as negative slopes indicate a line sloping downward.

Solve the exercises from Actividad 1.3.4. For EJERCICIO 1, calculate the slope and the equation of the line passing through each pair of points. For EJERCICIO 2, find the general equation of the line from the given point and slope.

Learn how to calculate the slope and equation of a line from pairs of points in Actividad 1.3.4. This exercise covers key concepts in algebra and geometry, such as the slope formula and point-slope form, suitable for high school students.

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