Question

Determine if this equation is perpendicular? -4x+2y=12 x+2y=6

Can you please show the steps. Thank you

Answer 1

These two equations represent line which are perpendicular.

Explanation:

Any equation of the form:
`color(white)("XXX")Ax+By=Ccolor(white)("XX")` has a slope of `color(white)("XX")-A/B`

Therefore
#{: (-4x+2y=12," has a slope of ",-(-4)/2=2), (," and",), (x+2y=6," has a slope of ",-1/2) :}#

Two lines are perpendicular if the slope of one is the negative inverse of the slope of the other. The negative inverse of `2` is `-1/2`, so these lines are perpendicular.