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

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Student Comments

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