|
Question 434640: If my equation is y=1/2x+6
would my the perpendicular of this equation be?
and what would the parallel of the equation be?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Equations, in and of themselves, do not have perpendiculars or parallels. The graphs of certain equations, those for which the graph is a straight line, have other graphs that are either perpendicular or parallel. The real problem with your question is that there are an infinite number of perpendicular lines to the graph of the given equation, and there are an infinite number of parallel lines to the graph of the given equation.
Perpendicular lines have slopes that are negative reciprocals. Parallel lines have equal slopes.
To represent all of the possible perpendiculars of the graph of your equation, take the negative reciprocal of  , namely  , and then specify a variable, say  to represent all possible intercepts.
Then
\,|\,y\ =\ -2x\ +\ \beta,\,\beta\ \in\ \mathbb{R}\right})
is a description of all possible sets of ordered pairs that represent lines perpendicular to the graph of the given equation.
Parallel lines have equal slopes, so:
\,|\,y\ =\ \frac{1}{2}x\ +\ \beta,\,\beta\ \in\ \mathbb{R},\,\beta\ \neq\ 6\right})
is a description of all possible sets of ordered pairs that represent lines parallel to the graph of the given equation. The exclusion  excludes the set of ordered pairs representing the graph of the given equation.
John
My calculator said it, I believe it, that settles it
|
|
|
| |
