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If a = -12/5, then 5x + 2y = 6 and 3x - ay = 4 are parallel.

True or False?

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Patrick S. | Conquering MathConquering Math
2
Thank you for your question Lindsey
 
 
If two lines are parallel then they have the same slope.
 
So the first thing we need to do is put each function into slope intercept form and compare the slopes.
 
 
5x + 2y = 6                                                                
 
Subtract 5x to both sides                                           
 
2y = -5x + 6                                                             
 
         divide 2 to each side                                          
 
         y = -5/2x + 3                                                     
 
        Slope = -5/2
          
 
 
3x - ay = 4
 
Substitute -12/5 for a
 
3x - (-12/5)y = 4
 
Subtract 3x to both sides
 
- (-12/5)y = -3x + 4
 
multiply -1 and -12/5
 
12/5y = -3x + 4
 
Multiply through by 5/12
 
y = -5/4x + 5/3
 
Slope = -5/4
 
 
-5/2 does not equal -5/4 therefore the line are not parallel
Vivian L. | Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACHMicrosoft Word/Excel/Outlook, essay comp...
3.0 3.0 (1 lesson ratings) (1)
1
Hi Lindsey;
Both equations are in standard form...
Ax+By=C, neither A nor B equal zero, and A is greater than zero.
The slope is -A/B.
5x + 2y = 6
Slope is -5/2
3x - ay = 4
Slope is -[(3/(-a)]
A negative of a negative is positive.  Therefore this is...
3/a
a=-12/5
Let's plug this in, and see if the result is -5/2...
[3/(-12/5)]
Let's flip -12/5 into -5/12, and multiply this by 3...
(3)(-5/12)
-15/12
Both the numerator and denominator are divisible by 3...
-5/4
The two equations do NOT have the same slope.
THE TWO EQUATIONS ARE NOT PARALLEL.
FALSE!!!!
Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
5.0 5.0 (3 lesson ratings) (3)
1
3x - (-12/5)y = 4
 
Multiply both sides by 5:
 
15x + 12y = 20
 
slope = -15/12 = -5/4
 
slope of 5x + 2y = 6 is -5/2
 
The slopes are not equal so the lines are not parallel.