To find the equation of the line that goes through the points \((6, -3)\) and \((2, -1)\), we first need to determine the slope (m) using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, \((x_1, y_1) = (6, -3)\) and \((x_2, y_2) = (2, -1)\).
Substituting the values:
\[ m = \frac{-1 - (-3)}{2 - 6} = \frac{-1 + 3}{2 - 6} = \frac{2}{-4} = -\frac{1}{2} \]
Next, we use the point-slope form of the equation of a line:
\[ y - y_1 = m(x - x_1) \]
Using the point \((6, -3)\):
\[ y - (-3) = -\frac{1}{2}(x - 6) \]
Simplifying:
\[ y + 3 = -\frac{1}{2}(x - 6) \] \[ y + 3 = -\frac{1}{2}x + 3 \] \[ y = -\frac{1}{2}x + 3 - 3 \] \[ y = -\frac{1}{2}x \]
Thus, the equation of the line that passes through the points \((6, -3)\) and \((2, -1)\) is:
\[ y = -\frac{1}{2}x \]
None of the options provided match this equation directly as written. However, if we consider variations, please verify them based on the provided options.