Question

Question 3 (Essay Worth 10 points)
(4.04 MC)
Part A: A graph passes through the points (0,4), (1,8), and (2, 10). Does this graph represent a linear function or a non-linear function? Explain your answer in words.
Part B: Write one example of a linear function and one example of a non-linear function. (Use x and y as the variables)

Answer 1

Therefore the graph represents a non linear function.

Example of a linear function

ax+by=c

Example of non linear function

y²= 4ax

Step-by-step explanation:

The equation of line which passes through the line (0,4)and(1,8) is

$y-y_1=\frac{y_1-y_2}{x_1-x_2}(x-x_1)$

$\Leftrightarrow y- 4=\frac{4-8}{0-1}(x-0)$             [ here $x_1=0 ,y_1=4$ and $x_2=1, y_2=8$]

$\Leftrightarrow y-4=4x$

$\Leftrightarrow y-4x-4=0$

If a line passes through the points(0,4) ,(1,8) and (2,10) .Then (2,10) will satisfies the equation of line.

L.H.S = 10 -4(2) -4

          =10-8-4

         =-2 ≠ R.H.S

Therefore the graph represents a non linear function.

Example of a linear function

ax+by=c

Example of non linear function

y²= 4ax