Graph the equation f(x)=6x

Question

1.Graph the equation f(x)=6x

 

2. determine whether the given ordered pair is a solution of the system of equation (2,-3) -2y=x+4, 5y=8x+1

Answer 1

1.  A graph of f(x)=6x is a line.  It goes through the origin (0,0) and has a slope of 6.  That means for each additional 1 of x, there is an additional 6 of f(x).  So, the point (1,6) is also on the line.  Plot these two points, and draw the line through them.  (note:  any two points on the line could be used, but these are pretty easy).

 2.  You have a choice:  either put the point (2,-3) into both equations and determine (yes or no) whether BOTH equations are still true or just “solve” (that means find the common point) the two equations and see whether it is (2,-3).  This is because two lines can intersect at one point, or no points (parallel lines), or else they are the same line.

Let’s put (2,-3) into the formulas:
     Does  -2(-3) = 2 + 4   ?
                 6     =   6    ?    yes

      Does  5(-3) = 8(2) + 1    ?
                 -15  = 17  ?      No!
 

Just for fun, let’s “solve” (find the actual common point):
       16y = 8x + 32     (first equation multiplied by 8)
        5y  =  8x + 1      (second equation)
     -------------------   (subtract the two equations)
       11y =  31            (this is elimination method)
             y = 31/11            (divide both sides by -11)

       2(31/11) = x + 4     (first equation)
       x = 62/11 – 44/11
       x = 18/11

Checking (very important):
   Is  2(31/11) = 18/11 + 4   ?
         62/11 = 18/11 + 44/11  ?
          62/11 = 62/11   ?    yes

   Is 5(31/11) = 8(18/11) + 1   ?
        155/11 =  155/11   ?  yes