To derive the equation of a line in the form \(y = mx\) that passes through the origin (0, 0) and one of the given points, we need to calculate the slope \(m\).
Using the points provided:
- Dot 1 = (3, 3)
- Dot 2 = (8, 8)
We can find the slope \(m\) using either of the dots.
- For Dot 1 (3, 3): \[ m = \frac{y_1 - y_0}{x_1 - x_0} = \frac{3 - 0}{3 - 0} = \frac{3}{3} = 1 \]
Therefore, the equation for the line passing through the origin is: \[ y = 1x \quad \text{or simply} \quad y = x \]
- For Dot 2 (8, 8): \[ m = \frac{8 - 0}{8 - 0} = \frac{8}{8} = 1 \]
Again, the equation for the line passing through the origin is: \[ y = 1x \quad \text{or simply} \quad y = x \]
Thus, the simplified equation for the line through the origin is: \[ y = x \]
The correct answer from the options provided is: \[ \boxed{y = x} \]