Answer:
The equation in the slope-intercept form will be:
![y=-\frac{5}{4}x+1](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B5%7D%7B4%7Dx%2B1)
Step-by-step explanation:
Given
As we know that the equation of a line in point-slope form 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)
substituting the values m = -5/4 and point = (8, -9)
![y-\left(-9\right)=\frac{-5}{4}\left(x-8\right)](https://tex.z-dn.net/?f=y-%5Cleft%28-9%5Cright%29%3D%5Cfrac%7B-5%7D%7B4%7D%5Cleft%28x-8%5Cright%29)
![y+9=\frac{-5}{4}\left(x-8\right)](https://tex.z-dn.net/?f=y%2B9%3D%5Cfrac%7B-5%7D%7B4%7D%5Cleft%28x-8%5Cright%29)
Writing the equation in slope-intercept form
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
where m is the slope, and b is the y-intercept
so the equation of the line in slope-intercept form becomes
![y+9=\frac{-5}{4}\left(x-8\right)](https://tex.z-dn.net/?f=y%2B9%3D%5Cfrac%7B-5%7D%7B4%7D%5Cleft%28x-8%5Cright%29)
subtract 9 from both sides
![y+9-9=\frac{-5}{4}\left(x-8\right)-9](https://tex.z-dn.net/?f=y%2B9-9%3D%5Cfrac%7B-5%7D%7B4%7D%5Cleft%28x-8%5Cright%29-9)
![y=-\frac{5}{4}x+1](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B5%7D%7B4%7Dx%2B1)
Therefore, the equation in the slope-intercept form will be:
![y=-\frac{5}{4}x+1](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B5%7D%7B4%7Dx%2B1)