To find the equation of the line that passes through the points \((-3, 0)\), \((0, -2)\), and \((3, -4)\), we can start by finding the slope (m) of the line using the coordinates of two of the points.
We can use points \((0, -2)\) and \((-3, 0)\) to calculate the slope. The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using \((0, -2)\) as \((x_1, y_1)\) and \((-3, 0)\) as \((x_2, y_2)\):
\[ m = \frac{-2 - 0}{0 - (-3)} = \frac{-2}{3} \]
Now that we have the slope \(m = -\frac{2}{3}\), we can use the point-slope form of a line equation:
\[ y - y_1 = m(x - x_1) \]
Using point \((0, -2)\):
\[ y - (-2) = -\frac{2}{3}(x - 0) \]
Simplifying this gives:
\[ y + 2 = -\frac{2}{3}x \] \[ y = -\frac{2}{3}x - 2 \]
Now, we can convert this equation into standard form \(Ax + By = C\).
Starting with:
\[ y = -\frac{2}{3}x - 2 \]
Multiply through by 3 to eliminate the fraction:
\[ 3y = -2x - 6 \]
Rearranging gives:
\[ 2x + 3y = -6 \]
Thus, the equation of the line in standard form is:
\[ 2x + 3y = -6 \]
So the correct answer is:
2x + 3y = –6
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