To find the equation of the line with a slope of \(-\frac{2}{3}\) that passes through the point \((-3, -1)\), we can use the point-slope form of the equation of a line, which is:
\[ y - y_1 = m(x - x_1) \]
where \((x_1, y_1)\) is the point the line passes through and \(m\) is the slope.
Given:
- Slope \(m = -\frac{2}{3}\)
- Point \((x_1, y_1) = (-3, -1)\)
Substituting the values into the point-slope formula:
\[ y - (-1) = -\frac{2}{3}(x - (-3)) \]
This simplifies to:
\[ y + 1 = -\frac{2}{3}(x + 3) \]
Now, distributing \(-\frac{2}{3}\):
\[ y + 1 = -\frac{2}{3}x - 2 \]
Next, we subtract \(1\) from both sides to solve for \(y\):
\[ y = -\frac{2}{3}x - 2 - 1 \]
\[ y = -\frac{2}{3}x - 3 \]
Thus, the equation of the line is:
\[ y = -\frac{2}{3}x - 3 \]
Among the provided choices, the correct option is:
y = negative two-thirds x minus 3.