First of all, let's consider the line, since it's simpler to graph: we draw the endpoints and connect them:
[tex]f(x)=2-\dfrac{3x}{4\pi} \implies f(0)=2,\quad f(2\pi)=\dfrac{1}{2}[/tex]
So, you just need to draw the points
[tex](0,2),\quad \left(2\pi, \dfrac{1}{2}\right)[/tex]
As for the trigonometric function, we have to start from the parent function [tex]y=\sin(x)[/tex] and derive the graph of its child function via transformations:
- When we multiply the whole function by 2, we stretch the graph vertically. So, the function has still period [tex]2\pi[/tex], but now it ranges from -2 to 2 instead of from -1 to 1 (amplitude 2)
- When we multiply the argument by 2, we compress the function horizontally. So, the new period becomes [tex]\pi[/tex], and the function makes two complete oscillations from 0 to [tex]2\pi[/tex]
You can see the two functions in the image below. You can also see that the two graphs cross 4 times, meaning that the equation
[tex]y_1=y_2[/tex] has four solutions.
