Question

Look at this function:

x y
−6 −13
−4 −9
−2 −5
0 −1


Mark said that the function is linear.

Jason said that the function is nonlinear.

Which of the following explains who is correct?

Answer 1

x values are increasing by 2
y values are increasing by 4
Mark is correct

Answer 2

As x coordinate of function is : -6, -4, -2, 0

And y coordinate of function is : -13, -9, -5,-1

If a function is linear it means

Slope will be same everywhere.

Slope between two points
`(x_(1),y_(1)) \text{and} (x_(2), y_(2))` is =
`(y_(2)-y_(1))/(x_(2) -x_(1))`

=
`(-9+13)/(-4+6)=(4)/(2)=2\\(-5+9)/(-2+4)=(4)/(2)=2\\\\(-1+5)/(0+2)=(4)/(2)=2\\\\(-1+13)/(0+6)=(12)/(6)=2`

So, between any two points slope are same i.e equal to 2.So it is a linear function.

So, Mark is right that the function is linear.