For this case we have that by definition, the equation of the line of the slope-intersection form is given by:
![y = mx + b](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20b)
Where:
m: It is the slope of the line
b: It is the cut-off point with the y axis
By definition, if two lines are perpendicular then the product of their slopes is -1.
We have the following equation of the line:
![y = 2x-5](https://tex.z-dn.net/?f=y%20%3D%202x-5)
Then ![m_ {1} = 2](https://tex.z-dn.net/?f=m_%20%7B1%7D%20%3D%202)
We find ![m_ {2}:](https://tex.z-dn.net/?f=m_%20%7B2%7D%3A)
![m_ {2} = \frac {-1} {m_ {1}}\\m_ {2} = \frac {-1} {2}\\m_ {2} = - \frac {1} {2}](https://tex.z-dn.net/?f=m_%20%7B2%7D%20%3D%20%5Cfrac%20%7B-1%7D%20%7Bm_%20%7B1%7D%7D%5C%5Cm_%20%7B2%7D%20%3D%20%5Cfrac%20%7B-1%7D%20%7B2%7D%5C%5Cm_%20%7B2%7D%20%3D%20-%20%5Cfrac%20%7B1%7D%20%7B2%7D)
Thus, the perpendicular line will be of the form:
![y = - \frac {1} {2} x + b](https://tex.z-dn.net/?f=y%20%3D%20-%20%5Cfrac%20%7B1%7D%20%7B2%7D%20x%20%2B%20b)
We substitute the given point and find "b":
![-2 = - \frac {1} {2} (8) + b](https://tex.z-dn.net/?f=-2%20%3D%20-%20%5Cfrac%20%7B1%7D%20%7B2%7D%20%288%29%20%2B%20b)
![-2 = -4 + b\\-2 + 4 = b\\b = 2](https://tex.z-dn.net/?f=-2%20%3D%20-4%20%2B%20b%5C%5C-2%20%2B%204%20%3D%20b%5C%5Cb%20%3D%202)
Finally, the equation is of the form:
![y = - \frac {1} {2} x + 2](https://tex.z-dn.net/?f=y%20%3D%20-%20%5Cfrac%20%7B1%7D%20%7B2%7D%20x%20%2B%202)
ANswer:
![y = - \frac {1} {2} x + 2](https://tex.z-dn.net/?f=y%20%3D%20-%20%5Cfrac%20%7B1%7D%20%7B2%7D%20x%20%2B%202)
Answer:
b
Step-by-step explanation:
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