Question

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?

Answer 1

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=

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\ {\text{slope between two points}}\\\\ \frac{-6+8}{-2+3}=2, \frac{-4+6}{-1+2}=2,\frac{0+4}{0+1}=4, \frac{0+8}{0+3}=\frac{8}{3}$

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.

Answer 2

Notice that for the first 3 point as x increases by 1 , y increases by 2 but for the last that is not true there is an increase of 1 in x but there is an increase of 4 in y. So the function is not linear so its either c or d - which one do you think it is?