As it is a linear relationship, we can graph the function based on its equation in the form:
[tex]y=mx+b[/tex]
where m is the slope and b is the y-intercept.
To calculate the slope we can choose any two points and display them in the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Choosing for example (2, 1) and (4, 2):
[tex]m=\frac{2-1}{4-2}[/tex][tex]m=\frac{1}{2}[/tex]
Therefore, our equation is:
[tex]y=\frac{1}{2}x+b[/tex]
To calculate b we have to choose again a point, for example, (2, 1) and replace it as follows:
[tex]1=\frac{1}{2}\cdot2+b[/tex][tex]1=1+b[/tex][tex]b=1-1=0[/tex]
Finally, our equation is:
[tex]y=\frac{1}{2}x[/tex]
We can use this equation to get other coordinates by choosing any value for x and calculating y. Finally, we get the coordinate (x, y), and to get the line we unite all the points in a line.
Answer:
[tex]y=\frac{1}{2}x[/tex]
