we know that
If two lines are parallel , then their slopes are the same
we will proceed to calculate the slope of each line to determine the solution.
The formula to calculate the slope m between two points of the line is equal to
[tex]m=\frac{(y2-y1)}{(x2-x1)}[/tex]
case N 1) line AB
Let
[tex]A(-4,3)\\B(4,3)[/tex]
substitute the values
[tex]m=\frac{(3-3)}{(4+4)}[/tex]
[tex]m=\frac{(0)}{(8)}[/tex]
[tex]m=0[/tex]
[tex]0\neq 3[/tex]
therefore
The line AB is not the solution
vase N 2) line FG
Let
[tex]F(-3,-1)\\G(3,-3)[/tex]
substitute the values
[tex]m=\frac{(-3+1)}{(3+3)}[/tex]
[tex]m=\frac{(-2)}{(6)}[/tex]
[tex]m=-1/3[/tex]
[tex]-1/3\neq 3[/tex]
therefore
The line EG is not the solution
case N 3) line CD
Let
[tex]C(-3,0)\\D(3,2)[/tex]
substitute the values
[tex]m=\frac{(2-0)}{(3+3)}[/tex]
[tex]m=\frac{(2)}{(6)}[/tex]
[tex]m=1/3[/tex]
[tex]1/3\neq 3[/tex]
therefore
The line CD is not the solution
case N 4) line HJ
Let
[tex]H(-1,-4)\\J(1,2)[/tex]
substitute the values
[tex]m=\frac{(2+4)}{(1+1)}[/tex]
[tex]m=\frac{(6)}{(2)}[/tex]
[tex]m=3[/tex]
[tex]3=3[/tex]
therefore
The line HJ is the solution
therefore
the answer is the option
line HJ
