SOLUTION: Which best describes the relationship between the lines with the equations 9x-2y=5 and -9x+9y=9? [A] parallel [B] perpendicular [C] neither parallel nor perpendicular [D] sam

Algebra ->  Points-lines-and-rays -> SOLUTION: Which best describes the relationship between the lines with the equations 9x-2y=5 and -9x+9y=9? [A] parallel [B] perpendicular [C] neither parallel nor perpendicular [D] sam      Log On


   

Question 970369: Which best describes the relationship between the lines with the equations 9x-2y=5 and -9x+9y=9?
[A] parallel
[B] perpendicular
[C] neither parallel nor perpendicular
[D] same line
Found 2 solutions by MathLover1, Boreal:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Which best describes the relationship between the lines with the equations +9x-2y=5 and -9x%2B9y=9?
[A] parallel
[B] perpendicular
[C] neither parallel nor perpendicular
[D] same line
to find out, we need a slope;as you know, two lines
that have same slope are parallel,and do not intercept, there is no solution
two lines that have slope negative reciprocal to each other are perpendicular
where the lines lie on top of each other, one equation can be rearranged to be the other equation precisely; this means when solving, you would get y=y and x=x, there are infinite solutions in this case (every point along the line would be a solution)
+9x-2y=5 and -9x%2B9y=9?
so, first write both equations in a slope-intercept form
9x-2y=5

9x-5=2y
y=%289%2F2%29x-5%2F5
y=%289%2F2%29x-1=> a slope is %289%2F2%29 and y-intercept is -1

and
-9x%2B9y=9....both sides divide by 9
-x%2By=1
y=x%2B1=> a slope is 1 and y-intercept is 1
So, both the lines have different slopes and different y- intercept which means the lines neither parallel nor perpendicular

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2Cx%2B1%2C+%289%2F2%29x-1%29+


that all leads us to the conclusion that your answer is: [C]

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Put this in form of y on left and whatever x will be on right. That will get you very close to what you need.
9x-2y=5
subtract 9x both sides
-2y=-9x+5
Divide by (-2)
y= -(9/2) x - 5/(2) don't worry about the constant. Find the slope. It is 9/2
Second equation
-9x +9y =9
Add 9x to both sides
9y=9x +9
divide by 9
y=x + 1
slope is 1
Slopes different, lines intersect.
Slopes not negative reciprocal (would need -2/9 or -1 for both) Not perpendicular.
Neither parallel nor perpendicular
+graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%2B1%2C-9x%2F2-5%2F2%29