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type the equation that shows the pattern among this set of ordered pairs

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3 Answers

ΔX      X    Y        ΔY
   2    [2    5]       4
         [4    9]      
  1     [5    11]     2
  2      [7    15]    4
 
 
 ΔY /ΔX  is given , the difference between coordinates of every 2 consecutive point is given
  
     in each case equal  4/2 = 2/1=2
 
    So these points are located on a line, with slope =2. 
 
     Y = 2x +b
 
  can place coordinate of any one of the points and find out the equation:
 
      5 = 2(2) + b
      b =1
 
      Y = 2X + 1
 
the slope is rise/run=(9-5)/(4-2)=4/2=2=m
you can use any two of the points; m=(15-11)/(7-5)=4/2=2 again
choose a point and use the point-slope form
y-15=2(x-7)
y-15=2x-14
y=2x-14+15
y=2x+1
if I choose another point...
y-11=2(x-5)
y-11=2x-10
y=2x-10+11
y=2x+1