Recall that the slope-intercept form of a line equation is in the form
[tex]\begin{gathered} y=mx+b \\ \text{where} \\ m\text{ is the slope} \\ b\text{ is the y-intercept} \end{gathered}[/tex]Given that we have the slope m = -1/4, and point (-8,3), substitute these two and solve for the y-intercept
[tex]\begin{gathered} m=-\frac{1}{4} \\ (x,y)=(-8,3) \\ \\ y=mx+b \\ 3=\Big(-\frac{1}{4}\Big)(-8)+b \\ 3=\frac{-8}{-4}+b \\ 3=2+b \\ 3-2=b \\ 1=b \\ b=1 \end{gathered}[/tex]We now have solved for the y-intercept, with m = -1/4, and b = 1, the equation of the line is
[tex]y=-\frac{1}{4}x+1[/tex]