To find the equation of the line that passes through the points (0, 0) and (9, 3), we first need to determine the slope (m) of the line. The slope can be calculated using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points (0, 0) and (9, 3):
\[ m = \frac{3 - 0}{9 - 0} = \frac{3}{9} = \frac{1}{3} \]
Now we have the slope (m) of the line, which is \(\frac{1}{3}\). The equation of a line can be written in point-slope form as:
\[ y = mx + b \]
Since the line passes through the origin (0, 0), the y-intercept (b) is 0. Therefore, we can write the equation as:
\[ y = \frac{1}{3}x + 0 \]
This further simplifies to:
\[ y = \frac{1}{3}x \]
Looking at the provided responses:
- \( y = x - 2 \)
- \( y = x - 4 \)
- \( y = x^3 \)
- \( y = 3x \)
None of these equations match \( y = \frac{1}{3}x \). However, the closest to the one we derived is actually not present among the responses.
The correct equation should be:
\[ y = \frac{1}{3}x \]
If there is a misunderstanding of the options or details, please confirm and check for any adjustments needed.