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 \(\boxed{y + 8 = -4(x - 7)}\) and in slope-intercept form is \(\boxed{y = -4x + 20}\).