Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form. Passing through \( (8,-7) \) and perpendicular to the line whose equation is \( y=\frac{1}{5} x+4 \) Write an equation for the line in point-slope form. (Simplify your answer. Use integers or fractions for any numbers in the equation.) Write an equation for the line in slope-intercept form. \( \square \) (Simplify your answer. Use integers or fractions for any numbers in the equation.)

To find the equation of the line that passes through the point \( (8, -7) \) and is perpendicular to the line given by \( y = \frac{1}{5} x + 4 \), we first need to identify the slope of the perpendicular line. The slope of the given line is \( \frac{1}{5} \), so the slope of the line we want is the negative reciprocal, which is \( -5 \). Using the point-slope form of the equation of a line, which is \( y - y_1 = m(x - x_1) \), we can substitute in our slope \( m = -5 \) and the point \( (x_1, y_1) = (8, -7) \): \( y - (-7) = -5(x - 8) \) Simplifying, we have: \( y + 7 = -5(x - 8) \) Now, for the slope-intercept form \( y = mx + b \), we will distribute and rearrange: \( y + 7 = -5x + 40 \) Subtracting 7 from both sides: \( y = -5x + 33 \) Summarizing: 1. In point-slope form: \( y + 7 = -5(x - 8) \) 2. In slope-intercept form: \( y = -5x + 33 \)