Find the equation of straight line passing thro... - JAMB Mathematics 2023 Question

To find the equation of a line perpendicular to the given line \(3x + 2y + 4 = 0\) and passing through the point (2, 3), we need to follow these steps:

1. Find the slope (m) of the given line. The slope of the given line \(ax + by + c = 0\) is given by \(-\frac{a}{b}\).
2. Find the negative reciprocal of the slope found in step 1. This will be the slope of the line perpendicular to the given line.
3. Use the point-slope form of the equation of a line: \((y - y_1) = m(x - x_1)\), where \((x_1, y_1)\) is the given point and \(m\) is the slope found in step 2.
4. Simplify the equation into the desired form.

Let's go through the steps:

1. Given line: \(3x + 2y + 4 = 0\)
   Slope (m) = \(-\frac{3}{2}\)

2. Slope of the line perpendicular to the given line:
   Perpendicular slope = \(\frac{2}{3}\)

3. Point-slope form using the point (2, 3):
   \((y - 3) = \frac{2}{3}(x - 2)\)

4. Simplify the equation:
   \[3(y - 3) = 2(x - 2)\]
   \[3y - 9 = 2x - 4\]
   \[3y = 2x + 5\]