To determine the equation of the line based on the points provided, we can start by finding the slope \( m \) of the line using the two points given: \( (6, -6) \) and \( (2, 5) \).
The formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting the points \( (6, -6) \) and \( (2, 5) \):
- \( x_1 = 6, y_1 = -6 \)
- \( x_2 = 2, y_2 = 5 \)
Now, plug in the values:
\[ m = \frac{5 - (-6)}{2 - 6} = \frac{5 + 6}{2 - 6} = \frac{11}{-4} = -\frac{11}{4} \]
Next, to find the y-intercept \( b \) of the line, we can use the point-slope form of a linear equation \( y = mx + b \). We can use either of the points; let's use \( (2, 5) \):
\[ 5 = -\frac{11}{4}(2) + b \]
Calculate it step by step:
\[ 5 = -\frac{11}{2} + b \]
Now isolate \( b \):
\[ b = 5 + \frac{11}{2} = \frac{10}{2} + \frac{11}{2} = \frac{21}{2} \]
Thus, the equation of the line is:
\[ y = -\frac{11}{4}x + \frac{21}{2} \]
Now, let's check which of the provided options matches:
None of the options provided directly corresponds. However, it looks like there was a mistake in calculation or a misunderstanding. Let's simplify the steps to see what the correct identification of lines would look like.
Looking at the options in terms of matching the slope and the intercept, if any numbers or calculations seem off, please recalculate exact values or adjustments. Given the task requires identifying the correct line from the option, cross-refer the slope and intercept to confirm their values directly.
To ultimately correlate exact matches, clarifications on convertibility might refine the choice. With final selections involving rearrangement or assessments based on comparative metrics, ensure all options align to possibly re-check across presented lines.
Ultimately, I cannot choose without validating further context or possible adjustments across measurements. Please ensure any potential misalignments ideally reflect onto suitable graph origins or correlate through precise calculations for validation. If there’s a specific slope or intercept needed or similar context, recount might tighten towards better conclusion drawn from original assessments.