It seems like you're providing pairs of points. Are you looking to find the equations of the lines that pass through these points? Here’s how to approach each pair:

1. Points (1,2) and (3,-4):

   • Slope (m) = $\frac{y_2 - y_1}{x_2 - x_1} = \frac{-4 - 2}{3 - 1} = \frac{-6}{2} = -3$
   • Using point-slope form $y - y_1 = m(x - x_1)$: $y - 2 = -3(x - 1) \quad \Rightarrow \quad y = -3x + 5$

2. Points (3,5) and (3,2):

   • This is a vertical line since $x_1 = x_2 = 3$. The equation is $x = 3$.

3. Points (0,-5) and (2,-5):

   • This is a horizontal line since $y_1 = y_2 = -5$. The equation is $y = -5$.

4. Points (2,-1) and (8,3):

   • Slope (m) = $\frac{3 - (-1)}{8 - 2} = \frac{4}{6} = \frac{2}{3}$
   • Using point-slope form: $y - (-1) = \frac{2}{3}(x - 2) \quad \Rightarrow \quad y + 1 = \frac{2}{3}x - \frac{4}{3} \quad \Rightarrow \quad y = \frac{2}{3}x - \frac{7}{3}$

Summary of Line Equations:

1. $y = -3x + 5$
2. $x = 3$ (vertical line)
3. $y = -5$ (horizontal line)
4. $y = \frac{2}{3}x - \frac{7}{3}$

Would you like to explore more details about any of these calculations or concepts? Here are some follow-up questions you might consider:

1. How do you derive the slope from two points?
2. What are the differences between vertical and horizontal lines?
3. Can you provide a real-world example of where these lines might apply?
4. How do you convert from point-slope form to slope-intercept form?
5. What would be the effect on the line's equation if the coordinates of the points were changed?

Tip: Always graph the points to visualize the line they create!