Question

Find M so that the lines with equations -2x + My = 5 and 4y + x = -9 are perpendicular.

Answer 1

Formulas  :  1 ) If ax + by + c = 0 is a line equation then the slope of that is -a/b --------> (1)

                    2) If two lines are perpendicular to each other then their slopes follew the equation

                        m1 X m2 = -1------ > (2)

Given Equations are

-2x + My = 5

4y + x = -9

Rewrite the above two equations

-2x + My - 5 = 0

   x + 4y + 9 = 0

Compare these two equations with Eq (1)

m1  =  -(-2) / M

m1  =  2/M

m2  =  -1/4.

Substitute m1  =  2/m and m2  =  -1/4 in Eq (2)

(2/M) X (-1/4)  =  -1

-2 / 4M  =  -1

-1/  2M  =  -1

-1  =  -2M

1  =  2M

M  =  1/2

Answer :

The value of M is 1/2.