First, we have to find the slope of the given equation. Let's solve for y.
[tex]\begin{gathered} 2x-8y=3 \\ -8y=3-2x \\ y=\frac{3-2x}{-8} \\ y=-\frac{3}{8}+\frac{x}{4} \end{gathered}[/tex]The coefficient of x is 1/4, which means its slope is 1/4.
Now, we use this slope, the point (10,2), and the point-slope formula to find the equation
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-2=\frac{1}{4}(x-10) \\ y=\frac{1}{4}x-\frac{10}{4}+2 \\ y=\frac{1}{4}x+\frac{-10+8}{4} \\ y=\frac{1}{4}x-\frac{2}{4} \\ y=\frac{1}{4}x-\frac{1}{2} \end{gathered}[/tex]