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Sagot :

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]