The standard form equation for a line is
[tex]y=mx+b[/tex]in which m represents the slope and b the y-intercept.
start putting the value of the slope into the equation
[tex]y=\frac{1}{4}x+b[/tex]although it is a fraction we repace it as if it was a whole number
then using (4,5) as (x,y) we can find b, the y-intercept
[tex]5=\frac{1}{4}(4)+b[/tex]simplify both sides of the equation
[tex]5=1+b[/tex]subtract 1 one on both sides in order to find b
[tex]\begin{gathered} 5-1=1+b-1 \\ 4=b \\ b=4 \end{gathered}[/tex]The equation of the line is
[tex]y=\frac{1}{4}x+4[/tex]