Answer:
[tex]2x-y=-3[/tex]
Step-by-step explanation:
step 1
Find the slope of the given line
we have
[tex]2x-y=6[/tex]
isolate the variable y
[tex]y=2x-6[/tex] ----> equation of the line in slope intercept form
The slope of the given line is [tex]m=2[/tex]
step 2
Find the slope of the parallel line to the given line
Remember that if two lines are parallel, then their slopes are the same
therefore
The slope of the parallel line to the given line is [tex]m=2[/tex]
step 3
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=2[/tex]
[tex]point\ (-6,-9)[/tex]
[tex]y+9=2(x+6)[/tex]
step 4
Convert to slope intercept form
isolate the variable y
[tex]y+9=2(x+6)\\y+9=2x+12\\y=2x+12-9\\y=2x+3[/tex]
step 5
Convert to standard form
[tex]AX+BY=C[/tex]
where
A is a positive integer
B and C are integer
[tex]y=2x+3\\2x-y=-3[/tex]
