Considering the definition of parallel and perpendicular line:
A linear equation o line can be expressed in the form y = mx + b.
where
Parallel lines are two lines that are always at the same distance from each other and that prolonged towards infinity never touch.
Two lines are parallel if they have the same slope and different y-intercepts. That is, they have the same value of m and different value of b.
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 9x+8y=-2. Expressed in the form y = mx + b, you get:
8y= -2 - 9x
y= (-9x -2)÷ 8
y= -[tex]\frac{9}{8}[/tex]x - [tex]\frac{1}{4}[/tex]
Two lines are parallel if they have the same slope. So, in this case, the parallel line has a slope of -[tex]\frac{9}{8}[/tex] and has a form of: y= -[tex]\frac{9}{8}[/tex]x + b
The line passes through the point (-3, 2). Replacing in the expression for parallel line:
2= -[tex]\frac{9}{8}[/tex]× (-3) + b
2= [tex]\frac{27}{8}[/tex] + b
2- [tex]\frac{27}{8}[/tex]= b
- [tex]\frac{11}{8}[/tex]= b
Finally, the equation of parallel line is y= -[tex]\frac{9}{8}[/tex]x - [tex]\frac{11}{8}[/tex].
The line is y= -[tex]\frac{9}{8}[/tex]x - [tex]\frac{1}{4}[/tex].
If you multiply the slopes of two perpendicular lines, you get –1. In this case, the line has a slope of -[tex]\frac{9}{8}[/tex]. So:
-[tex]\frac{9}{8}[/tex]× slope perpendicular line= -1
slope perpendicular line= (-1)÷ (-[tex]\frac{9}{8}[/tex])
slope perpendicular line= [tex]\frac{8}{9}[/tex]
So, the perpendicular line has a form of: y= [tex]\frac{8}{9}[/tex]x + b
The line passes through the point (-3, 2). Replacing in the expression for parallel line:
2= [tex]\frac{8}{9}[/tex]× (-3) + b
2= -[tex]\frac{8}{3}[/tex] + b
2+ [tex]\frac{8}{3}[/tex]= b
[tex]\frac{14}{3}[/tex]= b
Finally, the equation of of perpendicular line is y= [tex]\frac{8}{9}[/tex]x + [tex]\frac{14}{3}[/tex].
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