Firstly, we will find slope of the given lne
we can select any two points from the graph
(-4,-5) and (4,-1)
so, x1=-4 , y1=-5 m x2=4 , y2=-1
now, we can use formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
now, we can plug values
[tex]m=\frac{-1+5}{4+4}[/tex]
[tex]m=\frac{1}{2}[/tex]
(B)
we are given
line parallel to the nline shown
and we know that
slope of two parallel lines are always equal
so, slope will also be
[tex]m=\frac{1}{2}[/tex]
we have point as (3,4)
now, we can use point slope form of line
[tex]y-y_1=m(x-x_1)[/tex]
we can plug values
[tex]y-4=\frac{1}{2}(x-3)[/tex]
we get
[tex]y=\frac{1}{2}x+\frac{5}{2}[/tex]
(D)
we have point as (-3, 2)
and we know that
slope of perpendicular line is -1/m
so,
[tex]m_p=-2[/tex]
now, we can use point slope form of line
[tex]y-2=-2(x+3)[/tex]
we get
[tex]y=-2x-4[/tex].............Answer
