What is the equation of the line perpendicular to the line 2x + 3y = -6 and having Y-intercept 3?
3x - 2y = -6
Step 1 — Slope of given line: Rewriting \(2x+3y=-6\) as \(y=-\tfrac{2}{3}x-2\) gives slope \(m_1=-\tfrac{2}{3}\).
Step 2 — Perpendicular slope: \(m_2=-\dfrac{1}{m_1}=\dfrac{3}{2}\).
Step 3 — Apply y-intercept 3:
\[y=\tfrac{3}{2}x+3 \implies 2y=3x+6 \implies 3x-2y=-6\]
Therefore the equation is 3x - 2y = -6.
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