Answer:
perpendicular slope = [tex]-\frac{3}{2}[/tex]
Step-by-step explanation:
First, find the slope of the given equation. We know that [tex]y = \frac{2}{3} x+3[/tex] is in slope-intercept form because y is isolated and it is placed in the [tex]y = mx + b[/tex] format. In an equation written in slope-intercept form, the [tex]m[/tex], or the coefficient of the x-term, represents the slope. So, the slope of the given line is [tex]\frac{2}{3}[/tex].
Lines that are perpendicular to each other have slopes that are opposite reciprocals. So, we need to find the opposite reciprocal of [tex]\frac{2}{3}[/tex]. To do so, change its sign and switch the numerators and denominators. This gives us [tex]-\frac{3}{2}[/tex], so that must be the slope of the perpendicular line.
