Question

After plotting the given points on a graph, identify the equation of the function and also state that whether the function is linear or not.

x	1	0	2	3
y	22	10	34	46

• A. $y=12x+10$
  It is a non linear function
• B. $y=10x+12$
  It is a non linear function
• C. $y=12x+10$
  It is a linear function
• D. $y=10x+12$
  It is a linear function

Answer 1

The correct option is C $y=12x+10$

It is a linear function

x	1	0	2	3
y	22	10	34	46

Plotting the above points on a graph, we observe:


The given data represents a function as no input has more than one output

Function is given by: y = mx + c
(m = slope and c = y-intercept)

$\text{Slope}=\frac{\text{Change in y}}{\text{Change in x}}=\frac{22-10}{1-0}=\frac{34-22}{2-1}=12$

$\text{y-intercept = output when x = 0}$
$\Rightarrow \text{y-intercept =}10$

$\therefore \text{Function is given by:}y=12x+10$

A function is linear when the equation is of the form y = mx + c.

So the above function is linear.