To find the equation of the line that passes through the origin and has the same slope as the line that passes through the points (3, 3) and (8, 8), we first need to determine the slope (m) of the line.
Using the formula for slope:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
For the points (3, 3) and (8, 8):
- \(y_1 = 3\)
- \(y_2 = 8\)
- \(x_1 = 3\)
- \(x_2 = 8\)
Now plugging in the values:
\[ m = \frac{8 - 3}{8 - 3} = \frac{5}{5} = 1 \]
This means the slope of the line is 1.
Now, since we want the equation of the line that passes through the origin (0, 0) using the slope-intercept form \(y = mx\), we substitute \(m\) into the equation:
\[ y = 1x \implies y = x \]
So the final answer is:
y = x