To write the slope-intercept form of the equation of each line, we use the formula:

$y = mx + b$ where:

• $m$ is the slope,
• $b$ is the y-intercept.

Now, applying this to each problem:

1. Slope = -8, y-intercept = -5 $y = -8x - 5$

2. Slope = 0, y-intercept = 5 (since the slope is 0, this is a horizontal line) $y = 5$

3. Slope = \frac{9}{5}, y-intercept = -5 $y = \frac{9}{5}x - 5$

4. Slope = \frac{6}{5}, y-intercept = 4 $y = \frac{6}{5}x + 4$

Would you like further details on any of these, or have any questions?

Here are five related questions to deepen your understanding:

1. How do you interpret the slope and y-intercept of a line geometrically?
2. What happens to the equation if the slope is negative?
3. Can you find the equation of a vertical line? How is it different from the slope-intercept form?
4. How can you convert the slope-intercept form to standard form $Ax + By = C$?
5. How does changing the y-intercept affect the graph of the line?

Tip: When the slope is zero, the line is horizontal, and the equation simplifies to $y = b$, where $b$ is the y-intercept.