Answer:
The slope-intercept equation is:
![y=\frac{3}{2}x+1](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B3%7D%7B2%7Dx%2B1)
Step-by-step explanation:
Given the equation
![y-4=-\frac{2}{3}\left(x-6\right)](https://tex.z-dn.net/?f=y-4%3D-%5Cfrac%7B2%7D%7B3%7D%5Cleft%28x-6%5Cright%29)
comparing it with 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)
where m is the slope
- so the slope of the line is -2/3.
As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line, so
The slope of the perpendicular line will be: 3/2
The point-slope form of the equation of the perpendicular line that goes through (-2, -2) is:
![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)
![y-\left(-2\right)=\frac{3}{2}\left(x-\left(-2\right)\right)](https://tex.z-dn.net/?f=y-%5Cleft%28-2%5Cright%29%3D%5Cfrac%7B3%7D%7B2%7D%5Cleft%28x-%5Cleft%28-2%5Cright%29%5Cright%29)
![y+2=\frac{3}{2}\left(x+2\right)](https://tex.z-dn.net/?f=y%2B2%3D%5Cfrac%7B3%7D%7B2%7D%5Cleft%28x%2B2%5Cright%29)
writing the line equation in the slope-intercept form
![y+2=\frac{3}{2}\left(x+2\right)](https://tex.z-dn.net/?f=y%2B2%3D%5Cfrac%7B3%7D%7B2%7D%5Cleft%28x%2B2%5Cright%29)
subtract 2 from both sides
![y+2-2=\frac{3}{2}\left(x+2\right)-2](https://tex.z-dn.net/?f=y%2B2-2%3D%5Cfrac%7B3%7D%7B2%7D%5Cleft%28x%2B2%5Cright%29-2)
![y=\frac{3}{2}x+1](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B3%7D%7B2%7Dx%2B1)
Thus, the slope-intercept equation is:
![y=\frac{3}{2}x+1](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B3%7D%7B2%7Dx%2B1)
Here,
As the slope-intercept form is
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
where m is the slope and b is the y-intercept
so
![y=\frac{3}{2}x+1](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B3%7D%7B2%7Dx%2B1)
m=3/2
b = y-intercept = 1
Therefore, the slope-intercept equation is:
![y=\frac{3}{2}x+1](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B3%7D%7B2%7Dx%2B1)