Question

Determine whether the graphs of the following equations are parallel or perpendicular. explain.
22. 3x-9y=9
3y=x+12
2x-6y=12

Answer 1

http://www.mathsisfun.com/data/grapher-equation.html

Use that site to graph lines(:

Answer 2

NOTICE:
BEFORE READING THIS POST LOOK AT THE VERY BOTTOM OF THE POST FIRST so you know what a negative reciprocal, which is a word i use, is!





Ok so this is how you know if they are parallel or perpendicular.


If they are perpendicular there slopes would be the NEGATIVE RECIPROCALS of each other.

If they are parallel the slopes are equal.



So basically if the slope is \[m\]
The slope of the other line is \[-\frac{ 1 }{ m }\] if the lines are perpendicular




If they are parallel the slopes are equal.

So to see if your lines are parallel solve the equations for y to get them into slope-intercept form;\[(y = mx +b)\]
So for your equations they would be:
For the first equation: \[3x - 9y + 9 \] becomes \[y = \frac{ 1 }{ 3 }x - 1\]
For the second equation:\[3y = x+12\] becomes \[y = \frac{ 1 }{ 3 }x + 4\]
For the final equation:\[2x - 6y +12\] becomes \[y = \frac{ 1 }{ 3}x - 2\]
Baiscally i am solving your equations for y
In slope-intercept form \[y = mx+b\]
where \[m\] is the slope and \[b\] is the y-intercept




As you can see in this case "\[m\]"for all the equations is the same.


Remember how earlier i said if a line is parallel the slopes are the same in this case they are.
So your lines are parallel not perpendicular.


Because if they were perpendicular the slopes would be negative reciprocals of each other as i explained above in this case they are not so your lines are parallel.

ANSWER: THE LINES ARE PARALLEL!

Mystery solved!!

Thx hope this helped :)






P.S. the NEGATIVE RECIPROCAL for a number \[x\] is \[-\frac{ 1 }{ x }\]