Question

How you find the value of m so that the lines with equations −3y+2x=4 and mx+2y=3 are perpendicular?

Answer 1

Answer:

m=3

Step-by-step explanation:

For two linea to be perpendicular, there slopes must follow the identity:

m.m' = -1

Where,

m is the slope of any of the two lines

m' is that of other.

In support of the above identity, consider two lines as:

ax+ by+c =0 ---L1

dx+ey+f=0 -- L2

Having a,b,c,d,e and f as constants.

Slope of any given line is actually the ratio of negative the coefficient of x to y. That is:

Slope = -coefficient of x/coefficient of y

So for L1,

m = -a/b

And for L2:

m' = -d/e

Now by the identity:

m.m'=-1

(-a/b)(-d/e)=-1

=> ad+be=0

Now for the given lines:

(2)(-3)+(2)(m)=0

=> -3+m=0

That is;

m =3