Question

The black line is the graph of y=x. Which of these equations could represent the blue line?

Answer 1

Here we can see that the blue line cuts exactly half way through the angle that the black line makes with x axis

That is all the x values are halved

Which implies all the x value of the black line are divided by 2 to form the points on the blue line

so that give us the function

$y=\frac{1}{2} x$

Answer 2

Answer:

Option D.

Step-by-step explanation:

It is given that black line is the graph of y=x.

We need to find the equation of blue line.

Both lines passes through (0,0) it means y is directly proportional to x.

$y\propto x$

$y=kx$

where k is constant of proportionality.

From the given graph it is clear that the black line is steeper than the blue line. It mean k<1.

If k is a very small number then the line is equivalent to x-axis. So, k≠0.001.

It means the possible value of k is 1/2. So the equation of blue line is

$y=\dfrac{1}{2}x$

Therefore, the correct option is D.