Question

Write parallel to 2x-y=6, through (-6,-9) in a standard from equation

Answer 1

`2x-y=-3`

Explanation:

step 1

Find the slope of the given line

we have

`2x-y=6`

isolate the variable y

`y=2x-6` ----> equation of the line in slope intercept form

The slope of the given line is
`m=2`

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
`m=2`

step 3

Find the equation of the line in point slope form

`y-y1=m(x-x1)`

we have

`m=2`

`point\ (-6,-9)`

`y+9=2(x+6)`

step 4

Convert to slope intercept form

isolate the variable y

`y+9=2(x+6)\\y+9=2x+12\\y=2x+12-9\\y=2x+3`

step 5

Convert to standard form

`AX+BY=C`

where

A is a positive integer

B and C are integer

`y=2x+3\\2x-y=-3`