Answer:
the answer is Y=-1/2x - 2
Step-by-step explanation:
1. Y=-1/2x + 6 since both lines are parrellel they use the same slope
M= -1/2
and you put it in point slope form (y-y1) = M(x-x1)
use point (0,-2) becuase the line has to go through this point
(y-(-2)= -1/2(x-0) (y+2)= -1/2x then you change it in to slope intercept form
(y+2)= -1/2x
-2 -2
y=-1/2x -2
The equation of a line parallel to line EF in slope-intercept form is ,[tex]y=-\frac{1}{2}x-2[/tex]
The slope of parallel lines will be always same.
Given that,
The equation of line EF is, [tex]y = -\frac{1}{2} x + 6.[/tex]
Compare above equation with [tex]y=mx+c[/tex]
We get, [tex]Slope(m)=-\frac{1}{2}[/tex]
So that line parallel to line EF will also have slope of [tex]-\frac{1}{2}[/tex].
Equation of parallel line is,
[tex]y=-\frac{1}{2}x+c[/tex]
Substitute point (0, −2) in above equation.
We get, [tex]c=-2[/tex]
Hence, equation is, [tex]y=-\frac{1}{2}x-2[/tex]
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