Question

Classify each relation as either linear or non-linear. Explain your answers.
(a) y = 3x – 5 ________________________________
(b) y = 2x 2 – 3x ________________________________
( c) y = -2x

Answer 1

Given

Three function

(a)y=3x-5

(b)y=2x²-3x

(c)y=-2x

To check

which function is linear or non-linear

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

Note : See from web as latex not shown on app

Now plot several points in all three function and put into graph.If the graph shows straight line then it will be a linear function and if shows curved then the function is non-linear.

(a)

$\large \boxed{\begin{tabular}{c|c|c|c}x & 0 & 1 & 2 \\ \cline{1-4} y & -5 & -2 & 1\end{tabular}}$

The first function y=3x-5 is a linear as it's graph above shown in figure is in a straight line.

(b)

$\large \boxed{\begin{tabular}{c|c|c|c}x & 0 & 1 & 2 \\ \cline{1-4} y & 0 & -1 & 2\end{tabular}}$

The second function y= 2x²-3x is a non-linear as it's graph shown above in the figure is not in a straight line or it is curved.

(c)

$\large \boxed{\begin{tabular}{c|c|c|c}x & 0 & 1 & 2 \\ \cline{1-4} y & 0 & -2 & -4\end{tabular}}$

The third function y=-2x is a linear as it's graph shown above is a straight line.