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

##### 1 Answer

May 8, 2017

#### 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"#