The points a(2,b) and b(4,10) lie on a line. the line x + 3y - 6=0 is perpendicular to this line. what is the value of b?

The value of b is 6

Step-by-step explanation:

Given as :

The points of line AB is A  = ( 2 , b)   and B = ( 4 , 10 )

So , Slop of this line is ( m 1) =

Or,                                 ( m 1) =

Or,                                  ( m 1) =

Again, Another line is

x + 3y = 6

Or, 3y = - x + 6

Or   y =   x +  

SO, Slope of this line is ( m 2 ) =

∵  Both lines are perpendicular to each other

Then , ( m 1) × ( m 2) = - 1

or,       ( m 1 ) ×   = - 1

So,     ( m 1 ) = 3

Now,   ∵ ( m 1) =

          ∴   3     =

Or,          10 - b = 6

∴                  b = 10 - 6 = 4

Hence The value of b is 6  Answer

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step-by-step explanation: