To find the equation of the line that passes through the origin (0, 0) and is defined by the points of the right triangle, we first need to determine the slope of that line.
Given that the base of the right triangle is 8 units (along the x-axis) and the height is 5 units (along the y-axis), we can identify two key points that will help us determine the slope of the line.
The triangle has one vertex at the origin (0, 0), and the other vertex at (8, 5). The slope (m) of the line that passes through the origin and the point (8, 5) is calculated as follows:
\[ m = \frac{\text{change in y}}{\text{change in x}} = \frac{5 - 0}{8 - 0} = \frac{5}{8} \]
Since the line passes through the origin, its equation can be expressed in slope-intercept form as:
\[ y = mx + b \]
where \( m = \frac{5}{8} \) (the slope) and \( b = 0 \) (the y-intercept, since it passes through the origin). Therefore, the equation simplifies to:
\[ y = \frac{5}{8}x \]
However, this form is not in the options provided. Let's express the slope \( \frac{5}{8} \) in decimal form:
\[ \frac{5}{8} = 0.625 \]
Now let's compare this to the options given.
None of the provided equations directly represent the slope \( \frac{5}{8} \), but let's analyze each option:
A. \( y = 5x + 8 \) (slope = 5, not \(\frac{5}{8}\))
B. \( y = 85x \) (slope = 85, not \(\frac{5}{8}\))
C. \( y = 8x + 5 \) (slope = 8, not \(\frac{5}{8}\))
D. \( y = 58x \) (slope = 58, not \(\frac{5}{8}\))
None of these options contain the correct slope of \( \frac{5}{8} \).
If you have further details or constraints, please provide that information, as based on the calculation, the equation of the line should be \( y = \frac{5}{8}x \).