1. To find x-intercept you have to substitute y=0. Then
[tex]0=\dfrac{1}{3}x-6,\\ \\\dfrac{1}{3}x=6,\\ \\x=18.[/tex]
x-intercept is (18,0).
2. To find y-intercept you have to substitute x=0. Then
[tex]y=\dfrac{1}{3}\cdot 0-6,\\ \\y=-6.[/tex]
y-intercept is (0,-6).
3. The graph of the function (straight line) see in the attached diagram.