To find the equation of the line that passes through the origin (0,0) and the point (1,3), we can use the slope-intercept form of the equation of a line:
\[ y = mx + b \]
where \( m \) is the slope and \( b \) is the y-intercept. Since the line passes through the origin, the y-intercept \( b \) is 0.
Next, we need to calculate the slope \( m \). The slope is defined as the change in \( y \) divided by the change in \( x \):
\[ m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points (0,0) and (1,3):
\[ m = \frac{3 - 0}{1 - 0} = \frac{3}{1} = 3 \]
Now we can write the equation of the line:
\[ y = 3x \]
So, the correct equation of the line is:
y = 3x