We have the next equation
[tex]8x+2y=7[/tex]
First we need to isolate the y of the equation above
[tex]2y=-8x+7[/tex][tex]y=\frac{-8}{2}x+\frac{7}{2}[/tex][tex]y=-4x+\frac{7}{2}[/tex]
If a line is parallel to other they need to have the same slope
the equation in slope-intercept form is
[tex]y=mx+b[/tex]
where m is the slope and b is the y-intercept in the case of our equation the slope is m=-4
as we can in the solutions we need to know the value of the slopes in order to know if the y are or not parallel to the line given .
for the case of A. we need to isolate the y
[tex]\begin{gathered} y-1=4(x+4) \\ y=4x+16+1 \\ y=4x+6 \end{gathered}[/tex]
m=4 the slope is not the same as the equation given so this line is not parallel.
for the case of B. as we can see the slope is m=-4 the slope is equal to the line given so B is parallel to the line given.
for the case of C. we need to isolate the y
[tex]\begin{gathered} 16x+4y=9 \\ 4y=-16x+9 \\ y=\frac{-16}{4}x+\frac{9}{4} \\ y=-4x+\frac{9}{4} \end{gathered}[/tex]
as we can see the slope is m=-4 the slope is equal to the line given so C is parallel to the line given.
for the case of D as we can see the slope of this equation is m=-4 so is equal to the line given so D is parallel to the line given.
The lines that are parallel to the line given is B,C and D.
