To find the equation of the line that passes through the points \((-6, -6)\) and \((2, 5)\), we first need to calculate the slope \(m\) of the line using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting in the coordinates \( (x_1, y_1) = (-6, -6) \) and \( (x_2, y_2) = (2, 5) \):
\[ m = \frac{5 - (-6)}{2 - (-6)} = \frac{5 + 6}{2 + 6} = \frac{11}{8} \]
Next, we can use the point-slope form of the line equation \(y - y_1 = m(x - x_1)\). Using point \((-6, -6)\):
\[ y - (-6) = \frac{11}{8}(x - (-6)) \] \[ y + 6 = \frac{11}{8}(x + 6) \] \[ y + 6 = \frac{11}{8}x + \frac{11}{8} \times 6 \] \[ y + 6 = \frac{11}{8}x + \frac{66}{8} \] \[ y = \frac{11}{8}x + \frac{66}{8} - 6 \] \[ y = \frac{11}{8}x + \frac{66}{8} - \frac{48}{8} \] \[ y = \frac{11}{8}x + \frac{18}{8} \] \[ y = \frac{11}{8}x + \frac{9}{4} \]
Thus, the equation of the line is:
\[ y = \frac{11}{8}x + \frac{9}{4} \]
Looking at the provided responses, the answer is:
y = 9/4 x + 11/8.