Which is the value of the coefficient a if the lines are parallel? 3x+y-5=0 and ax-4y+7=0

Expert Answers
hala718 eNotes educator| Certified Educator

3x + y -5 =0

The slope (m1) = -3

ax -4y  +7 =0

The slope (m2)= a/4

Since both line are parallel, then :

m1 = m2

-3 = a/4

==> a= -12

Then the equation is:

-12x -4y + 7 =0

giorgiana1976 | Student

If the 2 given lines are parallel, then the values of their slopes are equal.

The given equations are 3x+y-5=0 and ax-4y+7=0, so we'll have to put them in the standard from, which is y = mx+n.

We'll start with 3x+y-5=0. 

We'll isolate y to the left side:

y = -3x+5

So, the slope can be easily determined as m1 = -3.

That means that the second slope has the same value, m2 = -3.

We'll put the other equation into the standard form, isolating y to the left side:

ax-4y+7=0

-4y = -ax-7

We'll divide by -4:

y = (a/4)*x + 7/4

The slope is m2 = a/4

But m2 = -3, so a/4 = -3

a = -12

neela | Student

a1x+b1y+c1 and a2x+b2y+c2 are parallel , if  a1/a2 = b1/b2.

Using the above principle for the  given lines, 3x+y-5 = 0 and ax-4y+7 = 0,

3/a = 1/-4. Mutiply by 4a.

3*4 = -a. Or

a = -12