Question 75462
How to write an equation of a line with the given slope and y-intercept?


1. m = 3/7  b = -2         2. m = 9, b = 0       3. m = 0,  b =- 5


SOLUTION:  


The general equation of the line is given by:  


y = mx + b     ----------------(1) represents the standard(general)equation.


where, m = represents the slope and b represents the y-intercept


1) m = 3/7  b = -2


Substituting these in the above equation, we have: 


y = (3/7)x +(-2) 


==> 7y = 3x - 14 


-------------------------------------------------------------------------------


2. m = 9, b = 0 


Substituting these values in the general eqn, we have: 


y = (9)x + 0 


==> y = 9x 


------------------------------------------------------------------------------


3. m = 0,  b =- 5


Substituting these values, we get: 


y = (0)x + (-5)  


==> y = - 5 

------------------------------------------------------------------------------


(II) How to write an equation of a line through the given points


1. (-1,1) (2,7)   2. (0,-5)(3,-2)  3. (6,11) (3,13) 



Solution:  The equation of the line when two points are given is calculated by using the formula: 


{{{(y - y1)/(x - x1) = (y2 - y1)/(x2 - x1)}}} 


or this can also be written as : 


(y - y1) = m (x - x1)  ------------------(2)


Where {{{ m = (y2 - y1)/(x2 - x1)}}} gives the slope of the eqn.


We first calculate the slope of the eqn and then substitute them in the eqn (2) 


--------------------
--------------------



1. (-1,1) (2,7) 


Here in this case m  = {{{(7 - 1)/(2 - (-1))}}}

               
              ==> m = {{{6/3}}} 


              ==>  m = 3


Substituting the point and the slope in the eqn (2), we get: 


y - 1 = 3( x - (-1))


y - 1 = 3(x + 1) 


y - 1 = 3x + 3 


y = 3x + 4 


----------------------------------------------


2. (0,-5)(3,-2) 


Here in this case m  = {{{(-2 -(-5))/(3 - 0)}}}

               
              ==> m = {{{3/3}}} 


              ==>  m = 1


Substituting the point and the slope in the eqn (2), we get: 


y - (-5) = 1( x - 0)


==> y + 5 = x  is the equation of the straight line.  


-----------------------------------------------------------------------------


3. (6,11) (3,13) 



Here in this case the slope of this line is given by: 


m = {{{(13 - 11)/(3 - 6)}}} 


m = {{{(2/-3)}}} 


Substituting this in the above formula, we get: 


{{{(y - 11) = -(2/3)(x - 6)}}} 



{{{ 3(y - 11) = -2(x - 6) }}}



3y - 33 = -2x + 12 


3y + 2x = 33 + 12 


3y + 2x = 45  


Hence, the solution. 





HAPPY CALCULATING!!!!!  :))