To find the equation of the line shown in the graph, we need to determine the slope (rise over run) and the y-intercept.

1. Finding the Slope:

   • The line passes through two clear points: $(0, 4)$ and $(7, 0)$.
   • The slope $m$ can be calculated by using the formula: $m = \frac{\text{change in y}}{\text{change in x}} = \frac{4 - 0}{0 - 7} = \frac{4}{-7} = -\frac{4}{7}$

2. Finding the Y-intercept:

   • The y-intercept (where the line crosses the y-axis) is at $y = 4$.

3. Equation of the Line:

   • The slope-intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
   • Plugging in the values: $y = -\frac{4}{7}x + 4$

So, the correct answer is: D. $y = -\frac{4}{7}x + 4$

Would you like further details on any part of the solution?

Here are some related questions for practice:

1. How do you determine the slope from two points on a line?
2. What is the significance of the y-intercept in the equation of a line?
3. How can you convert a line equation from slope-intercept form to standard form?
4. What happens to the line if you change only the y-intercept?
5. How do you find the x-intercept of a line given its equation?

Tip: Always plot the points on a graph if you're unsure about the slope—it can help you visualize the rise and run easily.