To determine the equation of the line that forms the hypotenuse of the right triangle, we need to use the coordinates of the points that define the triangle.
The triangle has one vertex at the origin \((0, 0)\), a base that goes along the x-axis (from \((0, 0)\) to \((7, 0)\)), and a height that goes up to the line at the point \((7, 4)\).
The slope \(m\) of the line that goes through these two points \((0, 0)\) and \((7, 4)\) can be calculated using the formula for the slope: \[ m = \frac{\text{change in y}}{\text{change in x}} = \frac{4 - 0}{7 - 0} = \frac{4}{7} \]
Using the slope-intercept form \(y = mx + b\), and since the line passes through the origin, the y-intercept \(b = 0\). Thus, the equation of the line becomes: \[ y = \frac{4}{7}x \]
The correct answer is: A. y = \frac{4}{7}x.