To find the slope \( m \) and the y-intercept \( b \) of the line from the graph in your image, we'll follow these steps:

### 1. Identify Two Points on the Line
To find the slope \( m \), we need to identify two clear points on the line. From the image, it seems the line passes through:

- Point 1: \( (0, 2) \) (where the line crosses the y-axis)
- Point 2: \( (2, 3) \) (another point on the line)

### 2. Calculate the Slope \( m \)
The slope \( m \) is calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \( (x_1, y_1) = (0, 2) \) and \( (x_2, y_2) = (2, 3) \):

\[
m = \frac{3 - 2}{2 - 0} = \frac{1}{2} = 0.5
\]

### 3. Identify the Y-Intercept \( b \)
The y-intercept \( b \) is the point where the line crosses the y-axis. From the graph, this point is \( (0, 2) \). Therefore, \( b = 2 \).

### Conclusion
- The slope \( m = 0.5 \)
- The y-intercept \( b = 2 \)

These values suggest that the equation of the line is:
\[
y = 0.5x + 2
\]

Would you like any further details, or do you have any other questions?

Here are some related questions you might consider:
1. How can we verify the slope using different points on the line?
2. What does the slope \( m = 0.5 \) indicate about the line's steepness?
3. How can we determine the equation of a line given any two points?
4. What changes would occur to the graph if \( m \) or \( b \) were different?
5. How do the slope and y-intercept relate to real-world scenarios?

**Tip:** Always cross-check your slope calculation by ensuring the points you choose are accurate and correctly interpreted from the graph.

Learn how to find the slope \( m \) and the y-intercept \( b \) of a line using two points methodically. This problem-solving guide covers the slope formula, identifying points on a graph, and calculating the equation of a line. Suitable for Grades 7-9 students.

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