The given equation is
[tex]y=-\frac{1}{4}x+8[/tex]The y-intercept of the new line is -10.
We have to find a new parallel line to the given equation, which means they must have the same slope.
Remember that the coefficient of x is the slope, so the slope of the given line is -1/4. This means the new line has a slope fo -1/4 because it's parallel.
So, we know that the new line has a slope of -1/4 and its y-intercept is -10. We use the slope-intercept form to write the equation.
[tex]\begin{gathered} y=mx+b \\ y=-\frac{1}{4}x-10 \end{gathered}[/tex]