Answer:
Equation in point-slope form : ![(y-0)=\frac{-3}{5}(x-3)](https://tex.z-dn.net/?f=%28y-0%29%3D%5Cfrac%7B-3%7D%7B5%7D%28x-3%29)
Equation in Slope-intercept form : ![y=\frac{-3}{5}x+\frac{9}{5}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B-3%7D%7B5%7Dx%2B%5Cfrac%7B9%7D%7B5%7D)
Step-by-step explanation:
Given point on the line are ( - 2 , 3 ) and ( 3 , 0 )
We need to write the equation of line in point-slope form and slope-intercept form.
Slope of the line = ![\frac{3-0}{-2-3}=\frac{-3}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B3-0%7D%7B-2-3%7D%3D%5Cfrac%7B-3%7D%7B5%7D)
Equation in Point Slope form is written as,
![(y-y_1)=m(x-x_1)](https://tex.z-dn.net/?f=%28y-y_1%29%3Dm%28x-x_1%29)
So, Equation in point-slope form : ![(y-0)=\frac{-3}{5}(x-3)](https://tex.z-dn.net/?f=%28y-0%29%3D%5Cfrac%7B-3%7D%7B5%7D%28x-3%29)
Equation in Slope-intercept form is written as,
![y=mx+c](https://tex.z-dn.net/?f=y%3Dmx%2Bc)
So, Equation in point-slope form :
![(y-0)=\frac{-3}{5}(x-3)](https://tex.z-dn.net/?f=%28y-0%29%3D%5Cfrac%7B-3%7D%7B5%7D%28x-3%29)
![(y-0)=\frac{-3}{5}(x-3)](https://tex.z-dn.net/?f=%28y-0%29%3D%5Cfrac%7B-3%7D%7B5%7D%28x-3%29)
![y=\frac{-3}{5}x-\frac{-3}{5}\times3](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B-3%7D%7B5%7Dx-%5Cfrac%7B-3%7D%7B5%7D%5Ctimes3)
![y=\frac{-3}{5}x+\frac{9}{5}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B-3%7D%7B5%7Dx%2B%5Cfrac%7B9%7D%7B5%7D)