1.        the table shows a linear function. x -5 -4 -3 -2 -1 0 1 2 3 f (x) -11 -5 3 13 21 29 37 45 53   (a)    determine the difference of outputs of any two inputs that are 1 unit apart. show your work. (b)    determine the difference of outputs of any two inputs that are 2 units apart. show your work. (c)    determine the difference of outputs of any two inputs that are 3 units apart. show your work. (d)    what do you notice about the ratios of the differences in the outputs to the input intervals? explain your answer.

a) I used the equation x=-5; f(x)=-11 and x=-4; f(x)=-3. We get the range = -3-(-11)=8

b) I used the equation x=-5; f(x)=-11 and x=-3; f(x)=5. We get the range = 5-(-11)=16

c) I used the equation x=-5; f(x)=-11 and x=-2; f(x)=13. We get the range = 13-(-11)=24

d) Range of input is equal with the ratios of the output. You can find the pattern of output above 8,16,and 24 can divided by 8 and give the result 1,2 and 3

an

y = 6x -3y -12

y +3y +12 = 6x

=> . x = { 2y / 3 +2 } this is equation of line in terms of x

=> . if line meets the x-axis the co-ordinates of meeting point would be ( x , 0 )

=> . x = 2 ( 0 ) / 3 + 2

=> . x = 2

so, the point is ( 2 , 0 )

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step-by-step explanation: