Question

The algorithms given below represent linear function. Which of the two algorithm(s) have zero output at the zero input?

• A. Algorithm 1
• B. Both of them
• C. None of them
• D. Algorithm 2

Answer 1

The correct option is D Algorithm 2

Let us consider Algorithm 1:

Values of x	Value of y
3	15
4	19
5	23

Consider any two coordinates, say (3,15) and (4,19)

$\text{Slope}=\frac{\text{Change in y}}{\text{Change in x}}=\frac{19-15}{4-3}$

$\Rightarrow \text{Slope = 4}$

Equation of straight line is y = mx + c

Putting the value of m, we get:
$y=4x+c$

Consider one point, say (3,15)

Substituting the values, we get:

$\Rightarrow 15=4\left(3\right)+c$

$\Rightarrow 15=12+c$

$\Rightarrow 3=c$

Therefore, the equation for Algorithm 1 will be y = 4x + 3

At x = 0,
$y=4\times 0+3\Rightarrow y=3$

Therefore, at zero input the output is 3. So it is not the correct option.

Let us consider Algorithm 2:

Value of x	Value of y
3	13.5
4	18
5	22.5

Consider any two coordinates, say (3,13.5) and (4,18)

$\text{Slope}=\frac{\text{Change in y}}{\text{Change in x}}=\frac{18-13.5}{4-3}$

$\Rightarrow \text{Slope = 4.5}$

Equation of straight line is y = mx + c

Putting the value of m, we get:
$y=4.5x+c$

Consider one point, say (5,22.5)

Substituting the values, we get:

$\Rightarrow 22.5=4.5\left(5\right)+c$

$\Rightarrow 22.5=22.5+c$

$\Rightarrow 0=c$

Therefore, the equation for Algorithm 2 will be y = 4.x + 3

At x = 0,
$y=4\times 0+0\Rightarrow y=0$

Therefore, at zero input the output is zero. So it is correct option.