Question

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.

Answer 1

Hello from MrBillDoesMath!

Answer:    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