https://file.aiquickdraw.com/mathbot/file/1727209053594gpoutnxm.jpg

To determine the equation of the line shown in the graph, we need to identify two key characteristics:

1. **Slope (m):** The steepness or angle of the line.
2. **Y-intercept (b):** Where the line crosses the y-axis.

### Step-by-Step Analysis:
1. **Y-intercept:** The graph shows the line crossing the y-axis at \( y = 7 \), so \( b = 7 \).

2. **Slope (m):** 
   - From the graph, let's pick two points to calculate the slope. 
   - One point is clearly \( (0, 7) \) (the y-intercept).
   - Another point could be \( (-5, 3) \).
   - The slope formula is:

   \[
   m = \frac{y_2 - y_1}{x_2 - x_1}
   \]

   Using points \( (0, 7) \) and \( (-5, 3) \):

   \[
   m = \frac{7 - 3}{0 - (-5)} = \frac{4}{5}
   \]

3. **Equation:** Now that we have the slope \( m = \frac{4}{5} \) and the y-intercept \( b = 7 \), we can write the equation in slope-intercept form:

   \[
   y = \frac{4}{5}x + 7
   \]

### Conclusion:
The equation of the line is \( y = \frac{4}{5}x + 7 \).

Do you have any questions, or would you like more details on any part of this process?

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Here are 5 related questions for further exploration:

1. How do we calculate the slope if the points on the line are not clearly defined?
2. What is the significance of the y-intercept in a real-world context?
3. How would the equation change if the slope were negative?
4. What happens to the graph if the y-intercept changes but the slope stays the same?
5. Can you find the x-intercept of this line? How?

**Tip:** Remember, the slope tells you how much the line rises (or falls) for each unit it moves horizontally.

This solution explains how to find the equation of a line from a graph by determining its slope and y-intercept. The problem covers key algebraic concepts like the slope formula and linear equations, suitable for students in Grades 7-9.

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