The way to plot the graph is to find both x-intercept and y-intercept. (Unless if it's a polynomial function which you need to find vertexes. But this one is linear so no vertex.)
(1) - Find x-intercept, substitute y = 0
[tex]y=3x+1\\0=3x+1\\-1=3x\\3x=-1\\x=-\frac{1}{3}[/tex]
Therefore, the graph intercepts x-axis at (-1/3, 0)
(2) - Find y-intercept, substitute x = 0
[tex]y=3x+1\\y=0+1\\y=1[/tex]
Therefore, the graph intercepts y-axis at (0,1)
The graph's picture is below
