Answer:
Part 1) [tex]y=-6x+4[/tex]
Part 2) [tex]y=-x-5[/tex]
Part 3) [tex]y=\frac{1}{3}x+4[/tex]
Part 4) [tex]y=\frac{1}{3}x-2[/tex]
Part 5) [tex]y=-2x-3[/tex]
Part 6) [tex]y=x+1[/tex]
Step-by-step explanation:
we know that
If two lines are parallel, then their slopes are equal
If two lines are perpendicular, then their slopes are opposite reciprocal
The equation of the line in slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-intercept
Part 1) through:(1,-2) parallel to y= -6x-5
The slope of the given line is m=-6
The slope of the parallel line is m=-6 (the slopes are the same)
substitute the given values in the general equation
[tex]-2=-6(1)+b[/tex]
solve for b
[tex]b=-2+6=4[/tex]
so
The linear equation in slope intercept form is equal to
[tex]y=-6x+4[/tex]
Part 2) through: (-2,-3) parallel to y=-x+3
The slope of the given line is m=-1
The slope of the parallel line is m=-1 (the slopes are the same)
substitute the given values in the general equation
[tex]-3=-1(-2)+b[/tex]
solve for b
[tex]b=-3-2=-5[/tex]
so
The linear equation in slope intercept form is equal to
[tex]y=-x-5[/tex]
Part 3) through(3,5), perp to y= -3x+5
The slope of the given line is m=-3
The slope of the perpendicular line is m=1/3 (the slopes are opposite reciprocal)
substitute the given values in the general equation
[tex]5=\frac{1}{3}(3)+b[/tex]
solve for b
[tex]b=5-1=4[/tex]
so
The linear equation in slope intercept form is equal to
[tex]y=\frac{1}{3}x+4[/tex]
Part 4) through:(3,-1) perp to y= -3x +3
The slope of the given line is m=-3
The slope of the perpendicular line is m=1/3 (the slopes are opposite reciprocal)
substitute the given values in the general equation
[tex]-1=\frac{1}{3}(3)+b[/tex]
solve for b
[tex]b=-1-1=-2[/tex]
so
The linear equation in slope intercept form is equal to
[tex]y=\frac{1}{3}x-2[/tex]
Part 5) (-2,1) perp to y= 1/2x -2
The slope of the given line is m=1/2
The slope of the perpendicular line is m=-2 (the slopes are opposite reciprocal)
substitute the given values in the general equation
[tex]1=-2(-2)+b[/tex]
solve for b
[tex]b=1-4=-3[/tex]
so
The linear equation in slope intercept form is equal to
[tex]y=-2x-3[/tex]
Part 6) through: (-5,-4) perp to y =-x+5
The slope of the given line is m=-1
The slope of the perpendicular line is m=1 (the slopes are opposite reciprocal)
substitute the given values in the general equation
[tex]-4=1(-5)+b[/tex]
solve for b
[tex]b=-4+5=1[/tex]
so
The linear equation in slope intercept form is equal to
[tex]y=x+1[/tex]
