Let's solve the examples given in the image step by step.

Example 28: Find the slope

The slope of a line in the equation $y = mx + b$ is the coefficient $m$ of $x$.

1. $y = -\frac{4}{3}x + 2$
   Slope (m): $-\frac{4}{3}$

2. $y = -\frac{3}{4}x + \frac{1}{2}$
   Slope (m): $-\frac{3}{4}$

3. $y = 5x - 1$
   Slope (m): $5$

4. $5y + x = 7$
   Rearrange to slope-intercept form ($y = mx + b$): $5y = -x + 7 \implies y = -\frac{1}{5}x + \frac{7}{5}$
   Slope (m): $-\frac{1}{5}$

Example 29: Rewrite in $Ax + By + C = 0$ form and find the slope

1. $3y = -2x - 9$
   Rearrange to $Ax + By + C = 0$:
   $2x + 3y + 9 = 0$
   Values: $A = 2$, $B = 3$, $C = 9$
   Slope (m): $-\frac{A}{B} = -\frac{2}{3}$

2. $3x - y + 5 = 0$
   Already in $Ax + By + C = 0$.
   Values: $A = 3$, $B = -1$, $C = 5$
   Slope (m): $-\frac{A}{B} = -\frac{3}{-1} = 3$

3. $3y + 9x = 6$
   Rearrange to $Ax + By + C = 0$:
   $9x + 3y - 6 = 0$
   Values: $A = 9$, $B = 3$, $C = -6$
   Slope (m): $-\frac{A}{B} = -\frac{9}{3} = -3$

Do you want further clarifications or detailed steps for any of these? Here are 5 related questions you might explore:

1. What is the slope of a line parallel to one of these equations?
2. How do you determine the $y$-intercept from the slope-intercept form?
3. How do you convert equations to $y = mx + b$ when $y$ is not isolated?
4. What is the relationship between slopes of perpendicular lines?
5. How does changing the value of $C$ in $Ax + By + C = 0$ affect the graph of the line?

Tip:

The slope of a line is always $-\frac{A}{B}$ when the equation is in the form $Ax + By + C = 0$.