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Write the equation of the line in the form . y= mx + c

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.

Write the equation of the line in the form y = mx + c

Learn how to write the equation of a line in the slope-intercept form (y = mx + c) by analyzing the slope and y-intercept from a graph. Suitable for students in Grades 7-9, this exercise covers key concepts in linear equations and graphing.

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