Is the relationship shown by the data linear? how can you tell if it is or is not? if so, model the data with an equation.

Hello from MrBillDoesMath!

   The relationship is linear. The equation is y = 2x + 19

Discussion:

When x changes from -7 to -5 ( and increment of of +2),  y changes from 5 to 9 ( an increment of +4). When x changes from 5 to -3 (an increment of +2) , y changes from 9 to 13 (an increment of +4)... and so on

So far, when x changes by 2, y changes by 4.  This means the data falls on a line (so is linear). In fact,

(change in y) /  (change in x) = 4/2 = 2 =  slope of line.

so  y = 2x + b. As the line passes through the point ( -7, 5)

5 = 2 (-7) + b    or

5 = -14 + b       or ( adding 14 to both sides)

5 + 14 = 19  = b.

Hence the equitation the line is  y = 2x + 19

Thank you,

MrB

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