Answer:
Part 1) [tex]y=-2x-1[/tex]
Part 2) [tex]y=-(1/2)x+(5/2)[/tex]
Step-by-step explanation:
Part 1)
we know that
If two lines are perpendicular
then
the product of their slopes is equal to minus one
so
[tex]m1*m2=-1[/tex]
Find the slope of the given line
we have
[tex]y=\frac{1}{2}x-1[/tex]
the slope of the given line is [tex]m1=(1/2)[/tex]
Find the slope of the line perpendicular to the given line
[tex](1/2)*m2=-1[/tex]
[tex]m2=-2[/tex]
Find the equation of the line into slope intercept form
[tex]y=mx+b[/tex]
we have
[tex]m=-2[/tex]
[tex]point (-2,3)[/tex]
substitute and solve for b
[tex]3=-2(-2)+b[/tex]
[tex]3=4+b[/tex]
[tex]b=-1[/tex]
The equation is equal to
[tex]y=-2x-1[/tex]
Part 2)
we know that
If two lines are perpendicular
then
the product of their slopes is equal to minus one
so
[tex]m1*m2=-1[/tex]
Find the slope of the given line
we have
[tex]y+1=2(x-3)[/tex] -----> equation of the line into point slope form
the slope of the given line is [tex]m1=2[/tex]
Find the slope of the line perpendicular to the given line
[tex](2)*m2=-1[/tex]
[tex]m2=-(1/2)[/tex]
Find the equation of the line into slope intercept form
[tex]y=mx+b[/tex]
we have
[tex]m=-(1/2)[/tex]
[tex]point (5,0)[/tex]
substitute and solve for b
[tex]0=(-1/2)(5)+b[/tex]
[tex]b=5/2[/tex]
the equation is equal to
[tex]y=-(1/2)x+(5/2)[/tex]
