Answer:
[tex] \large \boxed{y = - \frac{2}{3} x + 2}[/tex]
Step-by-step explanation:
both slopes multiply each others must equal to -1 for perpendicular.
[tex] \large{m_1m_2 = - 1}[/tex]
Let m1 = 3/2
[tex] \large{ \frac{3}{2} m_2 = - 1} \\ \large{3m_2 = - 2} \\ \large{m_2 = - \frac{2}{3} }[/tex]
Therefore -2/3 is perpendicular to 3/2. Because the line passes through (6,-2)
[tex] \large{y - y_1 = m(x - x_1)}[/tex]
Given (x1, y1) = ordered pair
Therefore (x1, y1) = (6,-2)
and m = - 2/3
[tex] \large{y + 2 = - \frac{2}{3} (x - 6)}[/tex]
Write in slope-intercept form.
[tex] \large{y = - \frac{2}{3} x + 4 - 2} \\ \large{y = - \frac{2}{3}x + 2}[/tex]
