Question

Through: (3, 3) and (-5, 4)

Answer 1

Hi,  

a line is define by  the following equation :    y = ax+b

where  a  is the slope, and  b the value for x = 0

so you have :        a*3 +b = 3   for the first point

                              a*(-5) +b = 4  for second point  

  so you have a system :      3a+b =3

                                              -5a+b = 4

so :       3a+b -(-5a) -b = 3-4

             3a+5a +b-b = -1

             8a = -1

                a = -1/8

then a = -1/8   so , in remplacing a  by it's  value  in one equation ,   b  is :             3(-1/8) +b = 3

 -3/8 +b = 3

           b = 3 +3/8

           b =  24/8 +3/8

          b =  27/8

         

let's check :     3 (-1/8) + 27/8 =  -3/8 +27/8 = 24/8 = 3

first point is correct  

                         -5( -1/8) + 27/8 =  5/8 +27/8 =  32/8 = 4

second point is correct  

line  is  y = -1/8X +27/8