8. Write a linear equation that is perpendicular to \( 2 x-5 y=5 \) and passes through the point \( (2,-9) \).

To find a linear equation that is perpendicular to \( 2x - 5y = 5 \), we first need the slope of the given line. Rewriting it in slope-intercept form (y = mx + b), we get \( y = \frac{2}{5}x - 1 \). The slope (m) of this line is \( \frac{2}{5} \). The slope of the perpendicular line will be the negative reciprocal, which is \( -\frac{5}{2} \). Now, using the point-slope form of a line \( y - y_1 = m(x - x_1) \) with the point \( (2, -9) \), we get: \( y + 9 = -\frac{5}{2}(x - 2) \). Simplifying this we arrive at the equation of the perpendicular line: \( y = -\frac{5}{2}x + 1 \).