hello
we are given 1 point with x and y co-ordinate and a slope, we can easily write down the equation of the line
standard equation of a straight line is
[tex]\begin{gathered} y=mx+c \\ m=\text{slope} \\ c=\text{intercept} \end{gathered}[/tex]to solve this problem, we need to find the intercept first
substitute the x and y co-ordinates in the equation
[tex]\begin{gathered} y=mx+c \\ m=\frac{1}{3} \\ y=5 \\ x=3 \\ 5=\frac{1}{3}(3)+c \\ 5=1+c \\ c=4 \end{gathered}[/tex]we know our intercept is equal to 4 and we can proceed to write out our equation
[tex]y=\frac{1}{3}x+4[/tex]we can leave it this way or multiply through by 3
[tex]3y=x+12[/tex]