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

Explanation:

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

`y-y_1=(y_1-y_2)/(x_1-x_2)(x-x_1)`

`\Leftrightarrow y- 4=(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