Answer:
[tex]y = \frac{3}{2}x + \frac{13}{2}[/tex]
Step-by-step explanation:
Perpendicular lines have negative reciprocals slopes, in which the product of their slopes result in -1.
Since the slope of the given line is m1 = -2/3, its negative reciprocal must be m2 = 3/2:
[tex]m_{1} *m_{2} = (-\frac{2}{3}) (\frac{3}{2}) = -1[/tex]
Next, we'll use the slope of the other line, m = 3/2, and the given point, (-3, 2) to solve for the y-intercept of the other line by substituting the values into the slope-intercept form:
y = mx + b
[tex]2 = \frac{3}{2}(-3) + b[/tex]
[tex]2 = -\frac{9}{2} + b[/tex]
Add 9/2 to both sides to isolate b:
[tex]2 + \frac{9}{2} = -\frac{9}{2} + \frac{9}{2}+ b[/tex]
[tex]\frac{13}{2} = b[/tex]
Therefore, the equation of the line perpendicular to [tex]y = -\frac{2}{3}x - 4[/tex] is:
[tex]y = \frac{3}{2}x + \frac{13}{2}[/tex]
