One positive effect of devolution is that it helps maintain a cohesive state. This means that it helps the state remained unified.
Answer:
![y = -\frac{1}{m}x + mc](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B1%7D%7Bm%7Dx%20%2B%20mc)
Explanation:
Given
![y = m(x + c)](https://tex.z-dn.net/?f=y%20%3D%20m%28x%20%2B%20c%29)
Required
Determine an equation of a perpendicular line but with the same y intercept
![y = m(x + c)](https://tex.z-dn.net/?f=y%20%3D%20m%28x%20%2B%20c%29)
Open bracket
![y = mx + mc](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20mc)
A linear equation is represented with:
![y = ax + b](https://tex.z-dn.net/?f=y%20%3D%20ax%20%2B%20b)
Where
![a = slope](https://tex.z-dn.net/?f=a%20%3D%20slope)
![b = y\ intercept](https://tex.z-dn.net/?f=b%20%3D%20y%5C%20intercept)
By comparison:
![a = m](https://tex.z-dn.net/?f=a%20%3D%20m)
![b = mc](https://tex.z-dn.net/?f=b%20%3D%20mc)
So, the slope of
is m
Because the new line is perpendicular to
, the relationship between their slopes is:
![a_2 = -\frac{1}{a_1}](https://tex.z-dn.net/?f=a_2%20%3D%20-%5Cfrac%7B1%7D%7Ba_1%7D)
Where
slope of the first equation
slope of the second equation
Substitute m for
in ![a_2 = -\frac{1}{a_1}](https://tex.z-dn.net/?f=a_2%20%3D%20-%5Cfrac%7B1%7D%7Ba_1%7D)
![a_2 = -\frac{1}{m}](https://tex.z-dn.net/?f=a_2%20%3D%20-%5Cfrac%7B1%7D%7Bm%7D)
Hence, the slope of the new equation is: ![-\frac{1}{m}](https://tex.z-dn.net/?f=-%5Cfrac%7B1%7D%7Bm%7D)
From the question, we understand that they have the same y intercept.
So, the equation of the new equation is:
![y = -\frac{1}{m}x + mc](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B1%7D%7Bm%7Dx%20%2B%20mc)