no need help with 8c anymore

Use Desmos.com and sketch the graphs.
b) basically is the number of points wherr they intersect.

what is y=2/pi x tho, like how to draw it during exam

y = 2/π x is a straight line, just like your usual y = 5x, y = 12x , y = 2x + 5 etc.

y = mx + c is your usual equation of a straight line.

In this case your m = 2/π and c = 0.

2/π is just 2 ÷ π
2 ÷ π ≈ 0.63661977....

Since you're asked to draw for the domain of 0 ≤ x ≤ 2π,

You know that when x = 0, y = 2/π × 0 = 0

When x = 2π, y = 2/π × 2π = 4

So for this straight line, just mark the coordinates (0,0) and (2π, 4) and join them.

usually just find the coordinates by inserting x=0 or x=2pi (or 3pi if the range ends at 3pi) into the equation then connect the 2points together?

It works for the equation of any straight line with a given domain.

If you had for example, y = 3x + 6 for the domain -3 ≤ x ≤ 10,

Sub x = -3 and x = 10 since they are the boundaries of your domain.

You'll get y = -3 and y = 36 respectively.

Plot (-3,-3) and (10,36) and join them.

Anywhere on this line, the gradient is the same.

Some of my students panick when they see such equations y = (2/pi) x. I think it’s because they are quite used to whole numbers or rational fractions as the gradient.

LockB, we draw such lines as usual. If we are provided with the range say 0 to 2pi, we can just substitute these limits to find the coordinates which would be (0, 0) and (2pi, 4).

The purpose of putting a pi in the denominator of the equation of the line is so that you have a nice y-value for sketching on your graph.

The 2/π makes the coordinates easy to plot.

As for 2/π itself, they should always be aware that π = 3.141592653...

It is a real number, and not a variable, so there's nothing to worry.

The setters could easily switch the question to another real transcendental number like e .

(though at this level we wouldn't expect things like the golden ratio (φ) = (1+√5) / 2 or Apéry's constant (ζ(3) ≈ 1.2020569031595942854...)