To find the equation of each line in the form $y = mx + c$, where $m$ is the slope and $c$ is the y-intercept, we need to analyze the lines one by one.

9) First Graph

• Slope (m): The line rises by 1 unit for every 2 units it moves to the right, so the slope $m = \frac{1}{2}$.
• Y-intercept (c): The line crosses the y-axis at $y = 0$.

Equation: $y = \frac{1}{2}x$.

10) Second Graph

• Slope (m): The line rises by 1 unit for every 1 unit it moves to the right, so the slope $m = 1$.
• Y-intercept (c): The line crosses the y-axis at $y = 0$.

Equation: $y = x$.

11) Third Graph

• Slope (m): The line falls by 1 unit for every 1 unit it moves to the right, so the slope $m = -1$.
• Y-intercept (c): The line crosses the y-axis at $y = 3$.

Equation: $y = -x + 3$.

12) Fourth Graph

• Slope (m): The line falls by 1 unit for every 2 units it moves to the right, so the slope $m = -\frac{1}{2}$.
• Y-intercept (c): The line crosses the y-axis at $y = 2$.

Equation: $y = -\frac{1}{2}x + 2$.

Let me know if you need further clarification or more details on the calculations!

Here are 5 related questions you could explore:

1. How do you calculate the slope of a line given two points on the line?
2. How does changing the slope affect the steepness of a line?
3. What does the y-intercept represent in a real-world context?
4. How would you graph a line given its equation in slope-intercept form?
5. How do parallel and perpendicular lines relate to each other in terms of slope?

Tip: The slope tells you how much the line rises (or falls) for every unit of horizontal movement. Always check the y-intercept to ensure you're placing the line correctly on the graph.