For a function \( f \), we are given that \( f(8)=1 \) and \( f^{\prime}(8)=2 \). What's the equation of the tangent line to the graph of \( f \) at \( x=8 \)

To find the equation of the tangent line to the graph of the function \( f \) at the point where \( x = 8 \), we can use the point-slope form of the equation of a line. The point-slope form is given by: \[ y - y_1 = m(x - x_1) \] where \( (x_1, y_1) \) is a point on the line and \( m \) is the slope of the line. From the information provided: - The point on the graph is \( (8, f(8)) = (8, 1) \). - The slope of the tangent line at this point is given by \( f'(8) = 2 \). Now we can substitute these values into the point-slope form: \[ y - 1 = 2(x - 8) \] Next, we can simplify this equation: \[ y - 1 = 2x - 16 \] Adding 1 to both sides gives: \[ y = 2x - 15 \] Thus, the equation of the tangent line to the graph of \( f \) at \( x = 8 \) is: \[ \boxed{y = 2x - 15} \]