Answer:
the slope of any line parallel to the given line is [tex]\frac{1}{2}[/tex]
[tex]y=\frac{1}{2}x-7[/tex]
perpendicular
Step-by-step explanation:
line [tex]y = \frac{1}{2}x + 5[/tex]
Slope of the given line is 1/2
Slope of parallel lines are same
the slope of any line parallel to the given line is [tex]\frac{1}{2}[/tex]
Equation of a line is y=mx+b
[tex]y-y1=m(x-x1)[/tex]
m=1/2 (x1,y1) is (0.-7)
[tex]y-y1=m(x-x1)[/tex]
[tex]y+7=\frac{1}{2}(x-0)[/tex]
[tex]y=\frac{1}{2}x-7[/tex]
[tex]x - 2y = 14[/tex]
Subtract x from both sides
[tex]- 2y = -x+14[/tex]
Divide both sides by -2
[tex]y=\frac{1}{2}x-7[/tex]
slope of both lines are same so they are parallel.
So the line is perpendicular to [tex]x - 2y = 14[/tex]
