Find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line. Perpendicular to the line \( x-5 y=-6 \); containing the point \( (0,9) \) The equation of the line is (Simplify your answer.)

To find the equation of a line perpendicular to the given line \(x - 5y = -6\), we first need to convert this equation to slope-intercept form. Rearranging gives us \(5y = x + 6\) or \(y = \frac{1}{5}x + \frac{6}{5}\). The slope of this line is \(\frac{1}{5}\). Therefore, the slope of the line we want, since it's perpendicular, will be the negative reciprocal: \(-5\). Now, we use the point-slope form of a line's equation, which is \(y - y_1 = m(x - x_1)\), where \((x_1, y_1)\) is the point (0, 9). Substituting in the values: \[ y - 9 = -5(x - 0) \] This simplifies to: \[ y - 9 = -5x \] \[ y = -5x + 9 \] So the equation of the line is \(y = -5x + 9\), which is in slope-intercept form. To express it in general form, we can rearrange it: \[ 5x + y = 9 \] Thus, the final equation of the line in general form is: \[ 5x + y = 9 \]