Let me extract the equations from the image and compute the slope and y-intercept for each equation.

Steps to Solve:

1. Rewrite each equation in the slope-intercept form ($y = mx + b$).
2. Identify the slope ($m$) and y-intercept ($b$).

Here’s the analysis for each equation:

1. $2x + 3y = 6$
   Rearrange to slope-intercept form:
   $3y = -2x + 6 \implies y = -\frac{2}{3}x + 2$
   Slope ($m$) = $-\frac{2}{3}$, y-intercept ($b$) = 2.

2. $3x + y = -2$
   Rearrange:
   $y = -3x - 2$
   Slope ($m$) = $-3$, y-intercept ($b$) = $-2$.

3. $x + 2y = -1$
   Rearrange:
   $2y = -x - 1 \implies y = -\frac{1}{2}x - \frac{1}{2}$
   Slope ($m$) = $-\frac{1}{2}$, y-intercept ($b$) = $-\frac{1}{2}$.

4. $4x - y = 3$
   Rearrange:
   $-y = -4x + 3 \implies y = 4x - 3$
   Slope ($m$) = 4, y-intercept ($b$) = $-3$.

5. $3x - 2y = 5$
   Rearrange:
   $-2y = -3x + 5 \implies y = \frac{3}{2}x - \frac{5}{2}$
   Slope ($m$) = $\frac{3}{2}$, y-intercept ($b$) = $-\frac{5}{2}$.

6. $x - y = 3$
   Rearrange:
   $-y = -x + 3 \implies y = x - 3$
   Slope ($m$) = 1, y-intercept ($b$) = $-3$.

7. $2x - 2y = -1$
   Rearrange:
   $-2y = -2x - 1 \implies y = x + \frac{1}{2}$
   Slope ($m$) = 1, y-intercept ($b$) = $\frac{1}{2}$.

8. $3x + 4y = -8$
   Rearrange:
   $4y = -3x - 8 \implies y = -\frac{3}{4}x - 2$
   Slope ($m$) = $-\frac{3}{4}$, y-intercept ($b$) = $-2$.

9. $2x - y = 0$
   Rearrange:
   $-y = -2x \implies y = 2x$
   Slope ($m$) = 2, y-intercept ($b$) = 0.

10. $x + y = 2$
    Rearrange:
    $y = -x + 2$
    Slope ($m$) = $-1$, y-intercept ($b$) = 2.

Let me know if you'd like detailed steps for any particular equation or need clarifications.

Here are 5 related questions:

1. How do you determine the slope and y-intercept from a linear equation graphically?
2. What is the relationship between parallel lines and their slopes?
3. How do you convert between standard form and slope-intercept form?
4. What does it mean if two equations have the same slope but different y-intercepts?
5. How can you verify the slope and y-intercept algebraically?

Tip: Always simplify the equation to the slope-intercept form for easier graphing and interpretation!