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?

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.