To find the equation of the line that passes through the points (0, 2) and (6, 4), we can first calculate the slope (m) of the line using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting the coordinates of the points (0, 2) and (6, 4):
\[ m = \frac{4 - 2}{6 - 0} = \frac{2}{6} = \frac{1}{3} \]
Now that we have the slope, we can use the point-slope form of the equation of a line, which is:
\[ y - y_1 = m(x - x_1) \]
Using the point (0, 2):
\[ y - 2 = \frac{1}{3}(x - 0) \]
This simplifies to:
\[ y - 2 = \frac{1}{3}x \] \[ y = \frac{1}{3}x + 2 \]
Thus, the equation of the line is:
\[ y = \frac{1}{3}x + 2 \]
The correct answer is y = one-third x + 2.