SOLUTION: Tell whether the lines are "parallel", "perpendicular", or "niether." 3x-9y=19 27x+12y=19

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Question 127454: Tell whether the lines are "parallel", "perpendicular", or "niether."
3x-9y=19
27x+12y=19
Found 2 solutions by checkley71, MathLover1:
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
Finding the slope will answer these questions using the line formula Y=mX +b. Where (m)=slope.
3x-9y=19 or -9y=-3x+19 or y=-3x/-9+19/-9 or y=x/3-19/9
This line has a slope of (1/3)
27x+12y=19 or 12y=-27x+19 or y=-27x/12+19/12
This line has a slope of (-27/12).
Seeing as these slopes are neither = nor a negative reciprocal of each other. Then these lines are neither perpendicular nor parallel.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


3x-9y=19

27x%2B12y=19





In order to graph these equations, we need to solve for y for each equation.




So let's solve for y on the first equation


3x-9y=19 Start with the given equation



-9y=19-3x Subtract 3+x from both sides



-9y=-3x%2B19 Rearrange the equation



y=%28-3x%2B19%29%2F%28-9%29 Divide both sides by -9



y=%28-3%2F-9%29x%2B%2819%29%2F%28-9%29 Break up the fraction



y=%281%2F3%29x-19%2F9 Reduce



Now lets graph y=%281%2F3%29x-19%2F9 (note: if you need help with graphing, check out this solver)



+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%281%2F3%29x-19%2F9%29+ Graph of y=%281%2F3%29x-19%2F9




So let's solve for y on the second equation


27x%2B12y=19 Start with the given equation



12y=19-27x Subtract 27+x from both sides



12y=-27x%2B19 Rearrange the equation



y=%28-27x%2B19%29%2F%2812%29 Divide both sides by 12



y=%28-27%2F12%29x%2B%2819%29%2F%2812%29 Break up the fraction



y=%28-9%2F4%29x%2B19%2F12 Reduce





Now lets add the graph of y=%28-9%2F4%29x%2B19%2F12 to our first plot to get:


Graph of y=%281%2F3%29x-19%2F9(red) and y=%28-9%2F4%29x%2B19%2F12(green)


From the graph, we can see that the two lines intersect at the point (133%2F93,-152%2F93) (note: you might have to adjust the window to see the intersection)


since parallel lines have the same slope m1=m2,you see that 1%2F3%3C%3E-9%2F4
so, these lines are not parallel
since perpendicular lines have slopes that are "opposite reciprocals" :
+m1=+-1%2Fm2
your slope are:
m1+=+1%2F3..........then perpendicular line should have m=-3
m2+=+-+9%2F4.........then perpendicular line should have m= 4/9
so, these lines are not perpendicular