The task is to write the equations of each line in slope-intercept form, $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. I'll solve these one by one.

1. Slope: $\frac{4}{5}$, y-intercept: $-8$
   Equation: $y = \frac{4}{5}x - 8$

2. Slope: $-1$, y-intercept: $-5$
   Equation: $y = -x - 5$

3. Slope: $\frac{7}{5}$, y-intercept: $-2$
   Equation: $y = \frac{7}{5}x - 2$

4. Slope: $\frac{7}{6}$, y-intercept: $-8$
   Equation: $y = \frac{7}{6}x - 8$

5. Slope: $8$, y-intercept: $-9$
   Equation: $y = 8x - 9$

6. Slope: $\frac{2}{7}$, y-intercept: $7$
   Equation: $y = \frac{2}{7}x + 7$

7. Slope: $-\frac{4}{3}$, y-intercept: $-9$
   Equation: $y = -\frac{4}{3}x - 9$

8. Slope: $\frac{8}{9}$, y-intercept: $12$
   Equation: $y = \frac{8}{9}x + 12$

9. Slope: $-\frac{1}{4}$, y-intercept: $9$
   Equation: $y = -\frac{1}{4}x + 9$

10. Slope: $\frac{7}{9}$, y-intercept: $-12$
    Equation: $y = \frac{7}{9}x - 12$

Would you like further explanations or additional help with any of these?

5 Related Questions:

1. How do you determine the slope and y-intercept from an equation in slope-intercept form?
2. What is the significance of the slope in a linear equation?
3. How can you graph a line given its slope and y-intercept?
4. What is the process for converting an equation in standard form to slope-intercept form?
5. How do different slopes affect the angle of a line?

Tip:

To check if your slope-intercept equation is correct, substitute a point on the line (e.g., where $x = 0$) to verify it satisfies the equation.