Question 513698
If lines are Perpendicular
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Standard Form of Equation of the line:
y=mx+b
Given
y + 8x = −14
rearrage the above equation according to the standard form
y=-8x-14
Compare above equation with the standard form equation
m=-8 and b=-14
Since lines are perpendicular multiplicatin of their slope will be (-1)
So slope of the required line will be (1/8)
Now we have a point(-8,1) and slope (1/8)of the line we can easily find required lines by putting these values in the equation of the straight line poin-slope form.
m=(y2-y1)/(x2-x1)
1/8=(y-1)/(x-(-8))
1/8=(y-1)/(x+8)
1(x+8)=8(y-1)
x+8=8y-8
8y-8=x+8
8y=x+8+8
8y=x+16
y=(x+16)/8
y=x/8+16/8
y=x/8+2
The standard form of the equation of the line
y=(1/8)x+2
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If lines are Parallel
=========================

Standard Form of Equation of the line:
y=mx+b
Given
y + 8x = −14
rearrage the above equation according to the standard form
y=-8x-14
Compare above equation with the standard form equation
m=-8 and b=-14
Since lines are parallel their slope will be same
So slope of the required line will be (-8)
Now we have a point(-8,1) and slope (-8)of the line we can easily find required lines by putting these values in the equation of the straight line poin-slope form.
m=(y2-y1)/(x2-x1)
-8=(y-1)/(x-(-8))
-8=(y-1)/(x+8)
-8(x+8)=(y-1)
-8x-64=y-1
-8x-64+1=y
-8x-63=y
y=-8x-63
Above equatoin is the required equation of the line in standard form.