Question

How do you write an equation of a line given point (1,-6) parallel to the line x+2y=6?

Answer 1

`y=-1/2x-11/2`

Explanation:

`" we require to know the following fact"`

`color(red)(bar(ul(|color(white)(2/2)color(black)(" parallel lines have equal slopes")color(white)(2/2)|)))`

`"express " x+2y=6" in the form "color(red)(bar(ul(|color(white)(2/2)color(black)( y=mx+b)color(white)(2/2)|)))`
where m represents the slope and b, the y-intercept

`"subtract x from both sides"`

`cancel(x)cancel(-x)+2y=6-x`

`rArr2y=6-x`

`"divide ALL terms by 2"`

`(cancel(2) y)/cancel(2)=6/2-1/2x`

`rArry=-1/2x+3larr" in form " y=mx+b`

`rArr"slope "=m=-1/2`

`"using " m=-1/2" and the point " (1,-6)`

`rArry=-1/2x+b`

`"to find b, substitute point into equation"`

`-6=-1/2+brArrb=-11/2`

`rArry=-1/2x-11/2" is the equation"`