Look at the following function: x y −3 −8 −2 −6 −1 −4 0 0 matt said that the function is linear. justine said that the function is nonlinear. which of the following explains who is correct?

Solution:

The elements of a function represented in terms of ordered pairs are (x,y): (-3,-8), (-2,-6), (-1,-4), (0,0).

You can check whether a function is linear or non linear by plotting the points on coordinate plane. If there is a unique line joining all these points then function is linear otherwise no linear.

Or there is a second way , by which you can check whether the points are collinear or by finding  slope between two points using point slope formula by taking any two points given.

Slope=

As slopes are unequal , points are nonlinear.

Justine is Right , while Matt is Wrong.

Another method:

Plot the points on coordinate plane

You will find that these points does not lie on a single line , so these points are non linear.

Third method:

X coordinate = -3 = -3+1 =-2, -2 +1=-1, -1+1=0, There is a gap or width of 1 unit between each x coordinate.

Y coordinate = -8=-8 +2=-6+2=-4, -4+2= -2 , but it is 0, So there is no fixed width or gap between two y values .

So , The function is Non linear.

the workers who do no drive has no reasonable reason to buy gasoline due to they don't have anything to use it for