Answer:
The equation of the line:
![y=\frac{3}{2}x+9](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B3%7D%7B2%7Dx%2B9)
Step-by-step explanation:
Given
We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:
slope = m = -2/3
perpendicular to m = -1/m
![=-\frac{1}{\left(\frac{-2}{3}\right)}=\frac{3}{2}](https://tex.z-dn.net/?f=%3D-%5Cfrac%7B1%7D%7B%5Cleft%28%5Cfrac%7B-2%7D%7B3%7D%5Cright%29%7D%3D%5Cfrac%7B3%7D%7B2%7D)
Using the point-slope form of the line equation
![y-y_1=m\left(x-x_1\right)](https://tex.z-dn.net/?f=y-y_1%3Dm%5Cleft%28x-x_1%5Cright%29)
substituting the values m = 3/2 and the point (-4, 3)
![y-3=\frac{3}{2}\left(x-\left(-4\right)\right)](https://tex.z-dn.net/?f=y-3%3D%5Cfrac%7B3%7D%7B2%7D%5Cleft%28x-%5Cleft%28-4%5Cright%29%5Cright%29)
![y-3=\frac{3}{2}\left(x+4\right)](https://tex.z-dn.net/?f=y-3%3D%5Cfrac%7B3%7D%7B2%7D%5Cleft%28x%2B4%5Cright%29)
Add 3 to both sides
![y-3+3=\frac{3}{2}\left(x+4\right)+3](https://tex.z-dn.net/?f=y-3%2B3%3D%5Cfrac%7B3%7D%7B2%7D%5Cleft%28x%2B4%5Cright%29%2B3)
![y=\frac{3}{2}x+9](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B3%7D%7B2%7Dx%2B9)
Thus, the equation of the line:
![y=\frac{3}{2}x+9](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B3%7D%7B2%7Dx%2B9)