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

The equation that could represent the equation of the blue line is $y=\frac{1}{2} x$

The standard form of the equation of a line is expressed as y = mx + b

m is the slope

b is the y-intercept

Since both lines cut the y axis at the origin, this means that the y-intercept will be zero.

Also, we can see from the graph that the blue line cuts exactly halfway through the angle that the black line makes with x-axis. This shows that the slope of the blue line is 1/2

Substituting m = 1/2 and b = 0 into the equation above, we will have;

$y =\frac{1}{2} x + 0\\y =\frac{1}{2} x$

Hence the equation that could represent the equation of the blue line is $y=\frac{1}{2} x$

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