Write the slope-intercept equation of the function \( f \) whose graph satisfies the given conditions. The graph of \( f \) passes through \( (-9,8) \) and is perpendicular to the line that has an \( x \)-intercept of 5 and a \( y \)-intercept of -15 . The equation of the function is (Use integers or fractions for any numbers in the equation.)

To find the slope-intercept equation of the function \( f \), we first need to determine the slope of the line that is perpendicular to the given line. The line with an \( x \)-intercept of 5 can be expressed as the point \((5, 0)\) and the \( y \)-intercept of -15 is the point \((0, -15)\). We can calculate the slope \( m \) of this line using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \): \[ m = \frac{0 - (-15)}{5 - 0} = \frac{15}{5} = 3. \] Since \( f \) is perpendicular to this line, the slope of \( f \) will be the negative reciprocal of 3, giving us: \[ m_f = -\frac{1}{3}. \] Now, we can use the point-slope form of the equation of a line, which is \( y - y_1 = m(x - x_1) \). We can plug in one point on the graph of \( f \) which is \((-9, 8)\) and the slope \(-\frac{1}{3}\) as follows: \[ y - 8 = -\frac{1}{3}(x + 9). \] Now, we distribute and simplify to find the slope-intercept form \( y = mx + b \): \[ y - 8 = -\frac{1}{3}x - 3, \] \[ y = -\frac{1}{3}x + 5. \] Thus, the equation of the function in slope-intercept form is: \[ f(x) = -\frac{1}{3}x + 5. \]