Answer:
Part 1) [tex]y=1.5x+5[/tex]
Part 2) [tex]y=-(2/3)x-(11/3)[/tex]
Part 3) [tex]y=0.25x+2.75[/tex]
Part 4) [tex]y=-2x+5[/tex]
Part 5) [tex]y=0.5x-1[/tex]
Part 6) The graph in the attached figure
Step-by-step explanation:
Part 1) we have
[tex]m=3/2=1.5[/tex]
[tex]point(-2,2)[/tex]
The equation of the line into point slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
substitute
[tex]y-2=1.5(x+2)[/tex]
[tex]y=1.5x+3+2[/tex]
[tex]y=1.5x+5[/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]
the slope of the line 1 is equal to
[tex]m1=1.5[/tex]
Find the slope m2
[tex]1.5*m2=-1[/tex]
[tex]m2=-2/3[/tex]
Find the equation of the line 2
we have
[tex]m2=-2/3[/tex]
[tex]point(-7,1)[/tex]
The equation of the line into point slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
substitute
[tex]y-1=(-2/3)(x+7)[/tex]
[tex]y=-(2/3)x-(14/3)+1[/tex]
[tex]y=-(2/3)x-(11/3)[/tex]
Part 3) we have
[tex]m=1/4=0.25[/tex]
[tex]point(1,3)[/tex]
The equation of the line into point slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
substitute
[tex]y-3=0.25(x-1)[/tex]
[tex]y=0.25x-0.25+3[/tex]
[tex]y=0.25x+2.75[/tex]
Part 4) we have
[tex]m=-2[/tex]
[tex]b=5[/tex] -----> y-intercept
we know that
The equation of the line into slope intercept form is equal to
[tex]y=mx+b[/tex]
substitute the values
[tex]y=-2x+5[/tex]
Part 5) we have that
The slope of the line 4 is equal to [tex]-2[/tex]
so
the slope of the line perpendicular to the line 4 is equal to
[tex]-2*m=-1\\m=(1/2)=0.5[/tex]
therefore
in this problem we have
[tex]m=0.5[/tex]
[tex]point(-2,-2)[/tex]
The equation of the line into point slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
substitute
[tex]y+2=0.5(x+2)[/tex]
[tex]y=0.5x+1-2[/tex]
[tex]y=0.5x-1[/tex]
Part 6)
using a graphing tool
see the attached figure
