Let's find the equation of the line perpendicular to $y=\frac{2}{3}x - 1$ that goes through the point $(3,4)$! 🎉 1️⃣ First, look at the slope of the given line. It is $\frac{2}{3}$. 2️⃣ The slope of a line perpendicular to it is the negative reciprocal. So, flip $\frac{2}{3}$ and change the sign: $$ m_{perp} = -\frac{3}{2} $$ 3️⃣ Now, use the point-slope form of a line with point $(3,4)$ and slope $-\frac{3}{2}$: $$ y - 4 = -\frac{3}{2}(x - 3) $$ 4️⃣ Let's simplify it step by step: $$ y - 4 = -\frac{3}{2}x + \frac{9}{2} $$ 5️⃣ Add 4 to both sides: $$ y = -\frac{3}{2}x + \frac{9}{2} + 4 $$ 6️⃣ Convert 4 to $\frac{8}{2}$ to add: $$ y = -\frac{3}{2}x + \frac{9}{2} + \frac{8}{2} = -\frac{3}{2}x + \frac{17}{2} $$ 🎯 Final answer: $$ y = -\frac{3}{2}x + \frac{17}{2} $$ Great job! You found the line that is perpendicular and goes through $(3,4)$! 🌟