To find the equation of the line that passes through the points (-6, -6) and (2, 5), we first need to determine the slope (m) of the line using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting the points (-6, -6) as \((x_1, y_1)\) and (2, 5) as \((x_2, y_2)\):
\[ m = \frac{5 - (-6)}{2 - (-6)} = \frac{5 + 6}{2 + 6} = \frac{11}{8} \]
Now that we have the slope \( m = \frac{11}{8} \), we can use the point-slope form of the equation of a line, which is:
\[ y - y_1 = m(x - x_1) \]
We'll use one of the points, say (-6, -6):
\[ y - (-6) = \frac{11}{8}(x - (-6)) \] \[ y + 6 = \frac{11}{8}(x + 6) \]
Expanding this:
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Distribute \(\frac{11}{8}\) across \((x + 6)\): \[ y + 6 = \frac{11}{8}x + \frac{11}{8} \times 6 \] \[ y + 6 = \frac{11}{8}x + \frac{66}{8} \] \[ y + 6 = \frac{11}{8}x + \frac{33}{4} \] (since \( \frac{66}{8} = \frac{33}{4} \))
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Subtract 6 from both sides: \[ y = \frac{11}{8}x + \frac{33}{4} - 6 \] \[ y = \frac{11}{8}x + \frac{33}{4} - \frac{24}{4} \] \[ y = \frac{11}{8}x + \frac{9}{4} \]
Thus, the equation of the line is:
\[ y = \frac{11}{8}x + \frac{9}{4} \]
Looking at the provided answer choices, the correct answer is:
y = \frac{11}{8}x + \frac{9}{4} (y is equal to 11 eighths x plus 9 fourths).