Question

Find the slope-intercept form for the line perpendicular to 2x –3y=-6 and passing through (4,–9)

Answer 1

For perpendicular lines, $m_1m_2 = -1$

From $2x-3y=-6$ , we have that $y=\frac{2}{3}x+2$

Let $m_1=\frac{2}{3}$

=> $m_2=\frac{-3}{2}$

$m_2=\frac{y-y_1}{x-x_1}$

$\frac{-3}{2}=\frac{y-(-9)}{x-4}=\frac{y+9}{x-4}$

=> $-3(x-4)=2(y+9)$

$12-3x=2y+18$

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