Considering the definition of perpendicular line, the equation of of perpendicular line is y= -[tex]\frac{1}{2}[/tex]x + [tex]\frac{13}{2}[/tex].
A linear equation o line can be expressed in the form y = mx + b.
where
x and y are coordinates of a point.
m is the slope.
b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.
Perpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.
In this case, the line is 2x-y=8. Expressed in the form y = mx + b, you get:
-y=8 - 2x
y= (-2x +8)÷ (-1)
y= 2x -8
If you multiply the slopes of two perpendicular lines, you get –1. In this case, the line has a slope of 2. So:
2× slope perpendicular line= -1
slope perpendicular line= (-1)÷ (2)
slope perpendicular line= -[tex]\frac{1}{2}[/tex]
So, the perpendicular line has a form of: y= -[tex]\frac{1}{2}[/tex]x + b
The line passes through the point (9, 2). Replacing in the expression for perpendicular line:
2= (-[tex]\frac{1}{2}[/tex])× 9 + b
2= -[tex]\frac{9}{2}[/tex] + b
2+ [tex]\frac{9}{2}[/tex]= b
[tex]\frac{13}{2}[/tex]= b
Finally, the equation of of perpendicular line is y= -[tex]\frac{1}{2}[/tex]x + [tex]\frac{13}{2}[/tex].
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