Answer:
y=-x+3
Step-by-step explanation:
The general slope-intercept equation of a line is y=mx+b where m is the slope and b represents the y intercept. y and x are simply a point the line passes through. In this case, y=x-5, meaning m=1 and b=-5.
In order to find the perpendicular slope, we should take the current slope's <u>negative reciprocal</u>. We have:
![-\frac{1}{1} =\\-1](https://tex.z-dn.net/?f=-%5Cfrac%7B1%7D%7B1%7D%20%3D%5C%5C-1)
Therefore, our perpendicular slope is -1. We now have equation:
![y=-x+b](https://tex.z-dn.net/?f=y%3D-x%2Bb)
We can plug in the known values of the point (-1,4) to solve for b.
![4=(-1)*(-1)+b\\4=1+b\\b=3](https://tex.z-dn.net/?f=4%3D%28-1%29%2A%28-1%29%2Bb%5C%5C4%3D1%2Bb%5C%5Cb%3D3)
If we now put what we found together, we have equation
![y=-x+3](https://tex.z-dn.net/?f=y%3D-x%2B3)
<em>I hope this helps! Let me know if you have any further questions :)</em>