JAMB Mathematics 2023 Paper

$3x + 2y + 4 = 0$

Rearrange:

$2y = -3x - 4$

Divide both sides by 2

y = $\frac{-3 \times -4}{2}$

y = $\frac{-3}{2} \times -2$

∴ the gradient of the line 3x + 2y + 4 = 0 is $\frac{-3}{2}$

If two lines are perpendicular to each other ∴ $m_1 x m_2$ = -1

Let $m_1 = \frac{-3}{2} \therefore m_2 = \frac{-1}{m_1} = \frac{-1}{\frac{-3}{2}} = \frac{2}{3}$

From the equation of a line which is given as m = $\frac{y - y_1}{x - x_1} \text{ where } (x_1, y_1) = (2,3)$

$\therefore \frac{2}{3} = \frac{y - 3}{x - 2}$

=3(y - 3) = 2(x - 2)

=3y - 9 = 2 x -4

=3y = 2 x -4 + 9

∴ 3y = 2x + 5