To find the equation of the line, we need to determine the slope ($m$) and the y-intercept ($b$) of the line.

Step 1: Calculate the Slope $m$

The slope of a line is given by: $m = \frac{\text{rise}}{\text{run}}$ In the given right triangle, the vertical side (rise) is $4$ and the horizontal side (run) is $7$.

So, $m = \frac{4}{7}$

Step 2: Determine the Equation

Using the slope-intercept form of the line $y = mx + b$, where $m = \frac{4}{7}$ and we assume the line passes through the origin, we get: $y = \frac{4}{7}x$

Conclusion

The correct answer is: B. $y = \frac{4}{7}x$

Would you like further details on any steps or have any other questions?

Here are some related questions to consider:

1. How is the slope determined when the line is not given directly in the equation?
2. How do we know if a line passes through the origin?
3. What is the impact of different slopes on the steepness of a line?
4. How would the equation change if the line had a negative slope?
5. How can we use a point on the line to verify an equation?

Tip: Remember, the slope $m$ tells you how many units the line goes up (or down if negative) for each unit it moves horizontally.