Answer: The equation for the line in point-slope form :![(y+2)=\dfrac{-6}{5}(x-4)](https://tex.z-dn.net/?f=%20%28y%2B2%29%3D%5Cdfrac%7B-6%7D%7B5%7D%28x-4%29)
The equation in slope-intercept form : ![y=\dfrac{-6}{5}x+\dfrac{14}{5}](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7B-6%7D%7B5%7Dx%2B%5Cdfrac%7B14%7D%7B5%7D)
Step-by-step explanation:
The equation of a line in point slope form passing through points (a,b) and (c,d) is given by :-
![(y-b)=\dfrac{d-b}{c-a}(x-a)](https://tex.z-dn.net/?f=%28y-b%29%3D%5Cdfrac%7Bd-b%7D%7Bc-a%7D%28x-a%29)
Now, the point slope form passing through points (4, -2) and (9, -8) is given by :-
![(y-(-2))=\dfrac{-8-(-2)}{9-4}(x-4)\\\\\Rightarrow (y+2)=\dfrac{-6}{5}(x-4)](https://tex.z-dn.net/?f=%28y-%28-2%29%29%3D%5Cdfrac%7B-8-%28-2%29%7D%7B9-4%7D%28x-4%29%5C%5C%5C%5C%5CRightarrow%20%28y%2B2%29%3D%5Cdfrac%7B-6%7D%7B5%7D%28x-4%29)
The equation for the line in point-slope form :![(y+2)=\dfrac{-6}{5}(x-4)](https://tex.z-dn.net/?f=%20%28y%2B2%29%3D%5Cdfrac%7B-6%7D%7B5%7D%28x-4%29)
Further if we simplify the equation , we get
![y+2=\dfrac{-6}{5}x+\dfrac{24}{5}\\\\\Rightarrow\ y=\dfrac{-6}{5}x+\dfrac{24}{5}-2\\\\\Rightarrow\ y=\dfrac{-6}{5}x+\dfrac{14}{5}](https://tex.z-dn.net/?f=%20y%2B2%3D%5Cdfrac%7B-6%7D%7B5%7Dx%2B%5Cdfrac%7B24%7D%7B5%7D%5C%5C%5C%5C%5CRightarrow%5C%20y%3D%5Cdfrac%7B-6%7D%7B5%7Dx%2B%5Cdfrac%7B24%7D%7B5%7D-2%5C%5C%5C%5C%5CRightarrow%5C%20y%3D%5Cdfrac%7B-6%7D%7B5%7Dx%2B%5Cdfrac%7B14%7D%7B5%7D)
The equation in slope-intercept form : ![y=\dfrac{-6}{5}x+\dfrac{14}{5}](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7B-6%7D%7B5%7Dx%2B%5Cdfrac%7B14%7D%7B5%7D)