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

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) (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) (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:

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

Start with the given equation

Subtract from both sides

Rearrange the equation

Divide both sides by

Break up the fraction

Reduce

Now lets graph (note: if you need help with graphing, check out this solver)

Graph of

So let's solve for y on the second equation

Start with the given equation

Subtract from both sides

Rearrange the equation

Divide both sides by

Break up the fraction

Reduce

Now lets add the graph of to our first plot to get:

Graph of (red) and (green)

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

since parallel lines have the same slope ,you see that
so, these lines are not parallel
since perpendicular lines have slopes that are "opposite reciprocals" :

your slope are:
..........then perpendicular line should have m=-3
.........then perpendicular line should have m= 4/9
so, these lines are not perpendicular
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