Problem

Find the equation of the line parallel to the line with equation \(2x - 3y = 5\) and passing through the point \((2, -1)\).

Answer

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Answer

Finally, we transform this into the standard form of a line equation, which is \(ax + by = c\). We get \(2x + 3y = 1\).

Steps

Step 1 :First, we find the slope of the given line. The slope of a line given by the equation \(ax + by = c\) is \(-a/b\). Therefore, the slope of the line \(2x - 3y = 5\) is \(-2/3\).

Step 2 :Since parallel lines have the same slope, the line we are looking for also has a slope of \(-2/3\).

Step 3 :Now, we use the point-slope form of a line, which is \(y - y_1 = m(x - x_1)\), where \(m\) is the slope and \((x_1, y_1)\) is a point on the line. Substituting the values we have, we get \(y - (-1) = -2/3(x - 2)\), which simplifies to \(y + 1 = -2/3x + 4/3\).

Step 4 :Finally, we transform this into the standard form of a line equation, which is \(ax + by = c\). We get \(2x + 3y = 1\).

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