Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form. Passing through (7,-8) and perpendicular to the line whose equation is y=1/4x+4

Step 1 ：The slope of the line given in the question is $\frac{1}{4}$.

Step 2 ：The slope of a line perpendicular to this line would be the negative reciprocal of this slope, which is -4.

Step 3 ：We can use this slope and the given point (7,-8) to write the equation of the line in point-slope form, which is $y-y1=m(x-x1)$, where m is the slope and $(x1,y1)$ is the given point.

Step 4 ：Substituting the values, we get $y+8=-4(x-7)$.

Step 5 ：We can rearrange this equation to get it in slope-intercept form, which is $y=mx+b$, where m is the slope and b is the y-intercept.

Step 6 ：Rearranging the equation, we get $y=-4x+20$.

Step 7 ：The equation of the line in point-slope form is $\boxed{{\displaystyle y+8=-4(x-7)}}$ and in slope-intercept form is $\boxed{{\displaystyle y=-4x+20}}$.